without this source of water in a prolonged power outage... Just something to consider....

VERY efficient. You do have to run the hot for a bit to get it going, though. Usually the shower heats up in about 30-45 secs. I don't know how that compares w/the 'always hot' old type but the utility savings (gas) has been great.

which are not as efficient as gas versions, but offer essentially the same pros and cons.

Short answer:
We love it.

Longer answer:
Get the proper size. THWH's are sized by (temperature rise) per (gallons per minute). For example, let's say a model is rated at 30 deg temperature rise at 2 gallons per minute. If your incoming water temp is 70 deg, your low-flow showerhead (2 gal per minute) will give you a 100 deg shower. Quite comfortable...until someone starts washing dishes or doing a load of whites in the laundry. This might be fine. It works for us.

Also, to make the most of its efficiency, set its heat so that you shower using ONLY the hot water...no point in heating the water to an uncomfortably high heat only to cool it down again.

teenage boy, did not get the hot showers for long. well... we all love our endlessly long hot showers and me pounding on doors to GET OUT. but, we love ours.

cost? dont know.

We had one installed in our remodel, and had to wait 5 weeks for the gas company to come out and up the pressure.

You also need to calculate how powerful a tank you will need - ***this is in no way a DIY project,*** from the selection of the unit, to the calculation of how much gas you will need, to the evaluation of how it will vent directly to the outdoors (we could not vent ours out the chimney that our conventional heater did because it was not large enough). Find a plumber that is very experienced in installing them.

They are not silent, so you won't want it near your bedroom if at all possible, but you will want it as close to your bathroom plumbing as possible.

required code in California. It's not a simple fix to put it where the current tank is.

I'd love to go tankless but it will require a dedicated gas line and new chimney -- $$$. If I install it on the other side of the house it will be easier and cheaper to install but the wait for hot water to the bathroom will be longer.

the same compact size: they just aren't manufactured anymore. The size mattered, because of the location of the water heater. So I had to decide whether to (1) switch to a compact electric heater (2) move to a larger gas heater in a different location or (3) go tankless

I went tankless. Frankly, it was rather more expensive to install than my electric option; comparing to my gas option is tricky, because that might have required some basement remodeling. I do notice the reduction in my gas bill, but the expected time for it to pay for itself might be two decades

Overall, I am happy with it, but there are a possible few issues. First, the tankless heater is much further from point-of-use than the old heater was, so I waste more water running the tap when I need hot water. Second, the maximum water temperature limit is set a bit lower than I might like; this was a choice I made during installation; the water temp is fine for all my standard uses, but if I wanted really really hot water from the tap, I couldn't get it myself by tinkering with the inside temperature control and would need to have the upper temperature limit adjusted by a pro. Third, the heater has a delay before kicking in, so I don't waste gas when somebody briefly turns on the hot faucet to rinse their fingers; this means that if I turn off the water briefly in the middle of a shower and then turn it back on, there's a little chunk of colder water down the pipe that reaches me a minute or two later

Ive also done a fair bit of reading. From what Ive read, it almost sounds like it might be better to go with several small ones, each devoted to a certain area(the bathroom, the kitchen, etc) as opposed to just replacing a standard WH with a large one.