Home in northern latitude of US has 2 Vertex 50 gallon heaters.
The Vertex that supplies hot to high-volume shower cannot keep up.

We confirmed there was a shortage of hot from unknown cause.
The Vertex might be undersized, or incoming water too cold, or water heater malfunctioning, or combination.
Troubleshoot, solutions and work arounds are offered.
Resource: Vertex service manual

Vertex Power Direct Vent heaters are Ultra Low Nox: or 14 ppm ... and.the incoming air supply comes from outdoors, and combustion vent pipe terminates outdoors.
Vertex Power Vent heater is Low Nox: or 20 ppm ... and.the: incoming air supply comes from inside home, and combustion vent pipe terminates outdoors.

Gene adds:  independent circuits means the heaters share incoming cold water line, but have no hot pipes in common.

-A plumbing problem could include faulty plumbing fixtures that allow too much water flow, high water pressure to house that increases water flow, non functioning check valve on recirculation system or elsewhere, recirculation pump adding cold instead of hot, bad single-handle faucet cartridge adding cold instead of hot.
-Overconsumption would be a shower that consumes more than the 75 gallon first hour rating of heater.

FYI: First hour is an industry term that estimates the amount of usable hot water from a single continuous draw. It does not always mean 100 gallons, or 75 gallon, it does not mean continuous hot water flow no matter what, nor that hot water will last an hour.

More detail: First hour represents a relative measure when comparing heaters before you buy. Manufacturers might fudge the numbers to get leg up on competitor.

My opinion:
a) Vertex 50 gallon condensing heater should deliver more than ordinary 40,0000 BTU, 50 gallon heater with a first hour delivery of 80 gallon.
b) Realistically, the 100,000 BTU burner, 94% thermal efficiency of condensing heaters, and 150° water temperature inside your tank, means the heater should be able to keep up with 1 shower and deliver at least 75-100 gallon of hot

More detail: One of the problems that might cause a shortage is if the two hot lines leaving heaters are somehow connected together ... except you report each heater is connected to separate 'circuit.'

The reason I say this, it that a 'common hot line' when house has 2 water heaters, and each heater services different areas... this can draw cold water and stop the flow of hot to one of the areas ... which is what you are experiencing. The solution would be break apart that common hot line.

Now if each heater is designed as a dedicated unit with no shared water lines, except incoming cold water, then that is best. And you would not combine the two heaters, unless there was a genuine shortage of hot water. (We confirmed a shortage from unknown cause, but the conversation took place in late winter from same latitude as Chicago which would have cold incoming water temps that would lower the expected first hour delivery).

-More detail: As a general rule, you can gain more hot from a fully heated tank by setting max temperature at 150°, which you have done already.
-When water is 150°, then more cold is mixed into the hot at your shower valve, to temper the bath-shower down to normal 104-110°F°.
-A mixing valve is a Common safety standard: if water heater temps are set to a potentially fatal hot water source (anything above 130°-140°F), then a mixing valve is installed on the hot water nipple as it leaves tank.

-A mixing valve is connected to hot water where it leaves tank, and then connected to cold water line. The mixing valve automatically adds or mixes cold water to the outgoing hot water, to temper it down to safe levels.
-Mixing valves are adjustable, and normally set to 120° ... or 110°-125°F. Typical bath-shower is 100-104°F
A malfunctioning mixing valve can allow too much cold water into the line, and can be a suspect in the plumbing problem you describe.
READ Advantages/ disadvantages mixing valve
Buy:
Water heater mixing valves

What we're looking for is a check valve on the direct return line.
A check valve is a one-way valve that lets the water flow one direction but not the other.
A faulty check valve on a recirculation return line (a spring-powered check valve where the spring failed, or a swing check valve installed vertically instead of horizontally) can cause cold water to enter hot water line.

Gene says:
Action 11) More detail: The recirculation system was barely mentioned among the answers, yet Warren reported there was a difference in first hour when it was running.
Apparently Warren experimented with turning recirculation system off since he knew there was a difference, but he did not report significant difference.
A recirculation system would reduce the amount of hot from a tank, so it is advisable to check the output with recirculation turned off.

If water heater thermostat is set higher than 120°, a mixing valve might reduce energy waste from running the recirculation system.

Why? The recirculation system is a loop, so it does not cause new cold water to enter the tank. But the 150° hot that leaves tank cools considerably while it travels the loop and then re-enters tank where it begins to re-heat, but also slightly cools overall water temperature inside tank. The thermostat does not trigger a heating cycle until tank temperature drops 6-8°F (wider range on some water heaters), which means water inside the Vertex can cool down to 140°F for example, depending on actual calibration of electronic controls. Using a recirculation system means heater will waste energy by running more to reheat water, but might also reduce first hour delivery if the tank was cooler due to wider-than-expected thermostat calibration (which is a good reason to have service tech check actual calibration range, or check it yourself using thermostat reading from TP valve and drain valve).

Buy: mixing valves
Resources:
Advantages mixing valve
Recirculation system

Answer:  
Your measurements show that your heater is delivering 68 gallon first hour, not 100, but close to 75. So if the spec sheet showing 100 gallon first hour is correct, then something is not right because you're getting less than an ordinary 40,000 BTU heater. Spec sheet for ordinary 50 gallon gas water heater with thermal efficiency of 70% and 40,000 BTU burner shows 80 gal first hour. Ordinary spec sheet

Vertex GDHE-50 should deliver more hot than an ordinary heater, based on the 100,000 BTU and 20% higher thermal efficiency. Of course, cold winter in Northern latitudes of US means water entering tank is probably 45-50°F which will reduce first hour delivery.

Is there a leak somewhere? Turn off all taps and put ear against pipe and listen for water leak. Water leak can run hot out of tank.
Check if any toilets are connected to hot line ... turn off all taps, flush and feel hot pipe top of heater to see if hot is leaving the tank ... sounds strange, but some guy bought two new heaters before he discovered the remodeler hooked toilet to hot pipe instead of cold.

Calculations: The first hour delivery calculation is as follows: Tank capacity x .7 (standard formula) + 129 gallon recovery (as shown in Vertex spec sheet) = 164 gallons first hour (The GDHE-50 spec sheet shows 100 gallon first hour)
If 164 is true... at 8 gallons a minute, that should give roughly 20 minutes ... of course it would be less with cold incoming water, maybe down to 15 minutes of hot ... but up because tank is fully heated to 150° and contains more heat energy.
If 100 gallon first hour is true as shown in Vertex spec sheet ... at 8 gallons a minute ... that should give 12 minutes ...
Which number is right? I cannot say.
Water-heater-Formulas-and-terminology.pdf

Gene says:
If overconsumption is the issue, I've had limited success solving problem for other folks without changing the heating equipment in some way because it takes a lot of BTUs from the burner, plus a large tank, to supply 'endless' hot water.
Folks with similar challenge should spec out the numbers beforehand, and install 2 Vertex units  plumbed in series or parallel, add a storage tank to the Vertex, add a tempering tank, or choose the largest 75-gallon Vertex GDHE-75, or install AO Smith commercial grade Cyclone 3-year warranty 250 gallon, 150,000-499,000 BTU condensing heater, or install a residential grade Polaris 1 year warranty 50 gallon with 199,000 BTU burner.
Large heater and large BTU rating, mean more first hour delivery.

Cyclone large volume commercial heaters are nearly 8' tall, and are the commercial version of the Vertex.
Resources:
Polaris spec sheet
Large volume Cyclone spec sheet
Storage tank with Vertex design sheet
Two water heaters

Answer: A mixing valve will help increase first hour delivery, plus Insulating the copper pipe will also help.

Answer: Yes. And you reported that there was a difference in first hour delivery when recirc pump was operating.

Answer: That is good idea.

It would be useful to know what temp incoming cold water is ... because my informal calculations show that a passive 50 gal tempering tank would help the Vertex deliver more hot water in winter, and perhaps year round ,.... probably your mechanical room is reasonably warm ... warmer than incoming water ....  50 gallon electric in Houston costs $420 (year 2020) ...making it a fairly cheap alternative. Install two 50 gallon electric in series with the Vertex and wire them up with a couple 10 gauge circuits, and you suddenly have 120 gallons more first hour. This is a genuine solution, and cheaper that buying new condensing heater that might require complete re-work of vent line etc, and cheaper than adding a storage tank plus additional circulating pump etc.
A 50 gallon gas heater could be used, and if it was fired up would deliver 80 gallons, except the gas heater can't be integrated into the Vertex vent line, and it would need it's own vent to the roof, plus it would require additional gas line ... lot of work. Electric heater is cheaper, and easier to turn on-off if usage is only needed in winter.

Be careful. You cannot have both ... it has to be either the ordinary incoming cold water supplies Vertex B, or the hot line from Vertex A supplies Vertex B, or you get cold water flowing into the hot line.
A double shut off valve could be added to give a choice between the cold water line and hot from Vertex A .... and that would give options if the shortage was seasonal or occasional.
Two 24 volt AC motorized ball valves (or use 24 volt sprinkler valves) could be used, and wired to home automation module (wifi, zwave). Automated valve might be reliable depending if signal reached the mechanical room, but the valves could also be hardwired to a delay timer that would be more reliable. A small 24 volt doorbell transformer, 2 valves, a spring-wound timer and doorbell wire required. General wiring

Except the burner is adding 100,000 BTU per hour ... or 100,000 x 1° per lb of water per hour ... or as shown in spec sheet, about 129 gallons recovery per hour ... which is 2.15 gallons per minute (but less since incoming water temps are low, and thermostat is set to 150° also it takes long to heat to set point) ... let's estimate that recovery is dialed down to 85 gallons per hour or 1.4 gallons for each minute. So for every 4 gallons of hot that are leaving tank per minute, another 1.4 gallons are being added while the tank is diminishing in temperature. In any case, the hot water should exceed the 8.75 by at least 1 gallon per minute, which means you should be getting minimum of 9.75 minutes of hot if the shower is consuming 8 gallons per minute.

Gene says:
You want to add a recirc pump between the two heaters ... probably too complicated .... couple issues strike me.
It's easy to choose the wrong pump ... if pump is too small, it won't move enough water ... too large (like 4 gallons a minute), it could cause a lot of bubbles and won't move water either ... and then how do you switch the pump on off? And how do you balance the flow if water is drawn from a tap vs a shower?
You could install a PID with probe taped to copper pipe that turned on the pump when temps on hot pipe indicate water is flowing on the hot line, except your existing recirc pump is constantly circulating water.
Resource: Add a PID
Buy: PID relay and thermocouple/ ITC-100HR/Temperature range :-50～250ºC

Gene says:
An amp switch could be added to a wire on the vertex, maybe on the blower motor, and when motor started, the amp switch would turn on the pump. But amp switch has to be on the hot wire, not both wires because hot and neutral together cancel each other. You could integrate the amp switch with a delay timer so the pump will only turn on after 8 minutes ... which would solve some problems ... I work with these type circuits most of the time, and they function reasonably well... Buy Amp switch/ Current switch/ current transducer

But another problem develops ... you need check valve, and who's to say the pressure of incoming cold water running at 4 gal per minute wouldn't hold the check valve closed ... it would if the pump was wrong. Certainly it holds the check valve closed on existing recirc line.
The whole idea is a long shot at best ... and lot more work than tempering tank(s), which would cause few problems ... but a tempering tank is low-impact and unimaginative, and some folks favor technological solutions.

Gene says:
Timer on the heater is probably unimportant except as a gizmo .... I think AO Smith sells an interface of some type for the Vertex .... they have building management software for the Cyclone series, which is their commercial version of the Vertex ... call them.
Instead of timer on heater, a timer on recirculation system and mixing valve will have benefit.
Disconnecting power to Vertex every day is usually not good idea ... because it would imitate a power outage, causing a surge event that could easily blow out the Vertex circuit board.

Do you have the Vertex plugged into surge outlet (not a surge module, a true surge outlet) ... the closer the surge protection, the more it protects. Multiple surge protection on one circuit is not a problem. I read that replacement circuit boards cost $1000 just for the board, plus labor.
I also hear that labor to replace parts on Vertex is equally expensive, and labor is not covered by warranty after first year.
Never connect Vertex, or any plug-in water heater to a GFCI or AFCI protected circuit. GFCI and AFCI will cause lockouts and error codes.
Buy: Surge outlet