My house, built new in 2002, has two tankless water heaters. One is a Bosch Aquastar 125B LP (with pilot) and the other is a Takagi TK1, sold as a Bosch Aquastar 240 (without pilot, requires electricity to run it). Both were purchased new from Controlled Energy Corp. I am satisfied with the 125B, less so with the Takagi.
Disclaimer: I'm not a licensed plumber so the futzing around I have done with this equipment has been ad hoc. I have not installed any water heater, with or without tank, in anybody else's house.
The 125B LP was leaky and fussy until I found that the licensed plumber who originally installed it put the control valve in wrong. Once I rebuilt it and installed it correctly this unit has been flawless. If you can rebuild a SU or Zenith-Stromberg carburetor you will understand how the control valve works. I am quite happy with this unit and it has required valve rebuilds on about a three-year rotation. My water is hard and is supplied by a well, treated with ozone in the 5000 gallon tank. The calcium carbonate in the water does not drop out of solution in the heater. It almost certainly would drop out in a tank-type heater because the water gets hotter locally in the tank than it does in the tankless units. This unit has a standing pilot. This negates some of the efficiency gains but see below for my Rant.
The Takagi is engineered a lot like many modern devices, with a computer and a bunch of electronics. This equipment has been troublesome. I've recently fought a problem with it to what appears to be a successful conclusion: partial lighting of the burner. This required me to remove and clean the burner, which is a bit of a trick on this device. The computer is badly confused by brown-outs and requires re-setting after some of them. The Takagi must have electricity to work. I bought it because I wanted to run a dual shower and could find no heater large enough to do that without it having a powered vent. Since power goes out frequently here, this is a problem. I've thought of cross-connecting the small heater but haven't done it yet.
If the Takagi isn't fixed by my recent work I am going to replace it with a large Paloma, which requires lower water pressure and has an atmospheric (non-powered) 7" vent, requiring no AC power to run (I believe it has batteries to run the sparker). The twenty Paloma heaters at my favorite hot springs resort receive next to no maintenance and have been there for years. All of them are mounted outside in a place where there is frost but few hard freezes.
Rant:
There's a tradeoff between old-school devices and modern ones. The modern ones can be more efficient as long as everything is working, but there are more parts in those and more parts means less reliability. I know of no exceptions. I do not buy appliances that have computers in them. The Takagi water heater was the one exception to my rule and I rue the day I bought it. I will not buy any equipment for my house that has anything more complicated than a discrete SCR in it any longer. Efficiency is good but anvil-like reliability is my first priority and I've never gotten that from modern, computer-controlled, optimized-to-a-fault equipment.