Given that assumption, it’s more energy-efficient to bypass one of them and shut it down.
"From this point on, the same amount of heat is trying to heat the same amount of water, so performance after startup should be similar.
(not sure my logic is flawless on this one.)"
Series will give you more initial draw but parallel will give you more overall production.
For the same reason series can give more initial draw #2 heater can not start recovery as soon as parallel can so the BTU’s are getting to business faster and more often on the parallel configuration. Of course usage dictates what configuration is best for each application.
Series. Outside water comes into water heater #1 (which is shut down/turned off) over night it warms up to say 60 degrees.
In the morning, water heater #2 provides hot water for your 15 gallon shower. Water heater #2 is now fed by water heater #1 and only has to bring the 60 degree water up to temp as it mixes with the existing hot water. If water heater #1 is completely taken off line, water heater #2 will be heating up water directly from the incoming line which will be colder and take more energy.