Hot bathtubs but cool showers - all thinkers welcome.

I've already posted this in r/ plumbing, I'm an engineer, and this appears to be an engineering problem. Strange problem for my landlords. The original water heater that came with their house would supply hot water to the shower/tubs (showers are on the walls above the bathtubs - standard) in all three bathrooms in the house. They replaced the water heater. Now, the bathtubs get hot water, but when switched to shower, the showers start hot but within ten seconds become cool. Every shower in the house has the same problem. The landlords replaced the water heater again, but the same problem exists. And here's the kicker - a neighbor across the street with a similarly built house came to have the same problem with the showers. What do you folks think? To me, it says that a water heater with unknown water flow characteristics is needed in order for the showers to be able to produce hot showers.