We went tankless (propane) 3 years ago rather than replacing our tank unit for the 4th time. The tankless unit cost quite a bit more than a tank heater would have cost, plus installation complexities drove up the total. Since there is not a 40- or 50-gallon reservoir of heat anymore, the pipes cool off and it takes a little longer for hot water to arrive at the tap, especially those further away from the source.
Those are the downsides. The upsides: there is no such thing as "running out of hot water". We use so little gas now (we have a gas stovetop too) that the last bill was $9.95! The propane folks informed us that they won't be refilling our tank as often anymore.
From all appearances this is a 'lifetime' product that can be maintained easily; I expect that this water heater will outlive me. And I'll never again go downstairs and find wet carpeting.
I can't speak to the electrics but I know enough about electricity to imagine that it would be possible to create an 'instant on' heat source for a tankless heater. I can also imagine that it would take a fairly serious wire gauge to feed it. I have a potential use for tankless electric and am curious to learn more. If you do decide to go tankless please keep us informed.