I don't know much about the electric type, but I installed a gas tankless a couple years ago.
Like you, I only use hot water for showers, which is where I think you save the most by switching to instant - if a household is using hot water constantly, the penalty for heating water 24/7 just to sit there and radiate said heat away again is smaller, percentagewise.
The one I got was very simple, with manual controls, and it cost substantially less upfront than a standard tank heater.
It reduced by use of gas rather dramatically (very roughly in half), and I only had a 5 gallon tank heater to begin with!
Definitely worth it.
I've noticed, (in online discussions, client's houses, and even from MMM himself) that the standard default is to buy a complicated instant heater filled with "features" - automatic temperature control, automatic pressure control, compensator, regulators, all sort of extra stuff which we never expected on tank heaters. All that stuff drives up the price and (according to an installer I spoke to) reduces the reliability. But that's all you will find offered by contractors and big box home improvement stores, so its all most people think exists.
You have to shop around internet style. I got mine (new) off of ebay. About $179 IIRC. Including shipping. Installed it myself in less than an hour.
If, like me, you adjust it to the temperature you need, so that you don't have to turn on the cold tap when you shower,
you have to adjust the temperature control between seasons.
All that said, the new wiring issue may change everything. Then again, for that price, if you have any gas lines in the house at all (stove? furnace? past appliances no longer in use?) you could route them to the water heater location for a lot less than $350 (more like $20 if you do the work yourself, which is easy), and just get a NG model instead.