What's the current cost situation on propane vs. electric? Nobody's mentioned that, and you have a propane tank.
Are those new-fangled instant on gas water heaters any good? I would think tub-filling would be a good application for it.
Nobody's mentioned the noise of the hp water heaters-they can run for a long time.
I've got an on-demand hot water heater, fueled by natural gas though. Mine is a Navien NPE-240A, 200,000BTU model, with built in recirculator.
Never run out of hot water
Smart controller that ensures the lines are full of hot water at common use times, ie morning showers.
No steel tank to rust out.
With an input temp just above freezing, and an output of 125F 4gal/min is all it puts out. Which I've found to be slow compared to tank style water heaters I've used for uses like, filling washing machine and bathtubs.
They need both gas and electric to function. Where with a tank style you still have hot water is left in the tank in the event of an outage.
Cost, mine was just over $4k, 3 times that of a traditional tank water heater.
Maintenance, the heat exchanger does need to be flushed with acid periodically to remove scale, this interval varies greatly with water quality.
Noise. The blower for the burner on mine does make some noise, especially if mounted to a wall and transmitted through the house, not a lot and this can be minimized with rubber isolators.