Provably cheapest and quickest solution! In our town, a permit for tank replacement can be pulled after the fact. Try to do that with replacing it with a tankless…
We live far enough, in a wooded enough area, that power outages happen more than we’d like. Given that even a sixty gallon tank won’t give hot water after several days of no power, we had a stand-by generator put in. Don’t know that it would run an electric tankless, but it does keep the propane fired one running.
Generators aren’t cheap and it requires an electrician to do the installation and cut-out for when the power is restored.
Interesting, @catahoula. Our natural gas tank cranked out endless hot water when we lost power for 6 days after one crazy storm. The hot water circulation did not work, but the tank kept on heating. That was what kept us put in the house instead of running to the nearest motel. 
Same as Bunsen - during Sandy the only thing still working in my house without electricity for many days was the gas powered hot water tank (oh and the Weber grill with its propane tank)
Following this thread, as our 26 yo gas water heater died 36 hours before we left for vacation! A couple of SG’s colleagus sang the praises of tankless, but I think continued hot water during a power outage will be a compelling argument for the status quo.
One more thing about a water heater—during an emergency, you could drink and use the water in the hot water tank. Can’t do the same thing with a tankless heater.
We have a hot water that runs off our boiler…no separate hot water tank. Regarding power outages…when we lose power, we also lose our well pump, so really showers don’t happen anyway. Well…except, we do have a small generator that can make this all work. First warm up the water…then use the well pump to get water for the shower.
We like not having a big tank in the basement, and knock on wood…we have never had a leak.
After having a 40 gallon electric Spring a leak in our old house, I said…never again! We had a swimming pool on our basement.
Our town requires a sump pump and water leak detector for basement tank OR boiler install. Major $$$ and PITA. Beats me why folks even want to do that. Put it in the garage which is by code required to be sloped so slightly for water runoff. Then any leak will be flowing outside… problem solved. Only if you don’t have an attached garage it can be an issue.
Our water heater is in a shed outside the kitchen door. If/when it leaks, it’s replaced.
Our tank-less propane (which seemed like a good idea at the time) wasn’t the entire reason we put in the standby generator, but that it doesn’t work without 120v made it a little easier to choke down - after a couple of outages.
If all you want in a power outage is hot water, go with a gas fired tank model. As pointed out, they still work.