[olddog]

I assumed you were talking about the small units that you locate near the ussage rather than one that supplied the entire house. I have only seen whole house units that were gas fired.

Pros
You only need to run cold water lines - saves half the plumbing cost for new installations.

Near instant hot water - no running water until you flush the lines from the tank.

No water tank to rust out.

No heat loss from a tank of hot water that is constantly kept hot.

Never run out of hot water, as it is heated as you use it.

One unit fails in one bathroom and the rest of the house and 2nd bathroom still function.

Cons
Takes a fairly large breaker and wire to supply the power. Todays wire cost could offset any savings in plumbing cost.

Takes a minimum water flow to turn it on, so you cannot trickle hot water slowly.

You need to install several units at different locations; kitchen, bath, washer.

Opinion:
We have a few at work in the mens room. I am so used to turning water on full hot everwhere else that I jump from the hot water hitting so fast. Other than that I like them. Europe almost exclusively has used them for decades. When I was there back in 1985, a lot of them would scald you, if you were not careful. I was there several times since, and never noticed any problems in the later years. I like them, and think they generally make good economic and enviromental since. Once you get used to the instant heat, you will like them.