The difference is "neithereverworks" Many studies show their life cost to be way over a tank type.
Show me the studies. (And not the crummy hatchet job from Consumer Reports, which was flawed beyond ball reason.)
Be sure to inclued the underlying assumptions about fuel pricing, the cost of money, volume of use, incoming water temps, etc. This is not a no-brainer, at least in the gas-fired case.
In the gas-fired case lifecycle cost can be break-even or slightly better for moderate use profiles in cool-water regions, but not necessarily for low-volume users in warmer areas such as FL. PG & E has done quite a bit of work vetting the lifecycle economics of gas fired tankless for their "typical" customers for the CA market, in part to determine the level of subsidy that the utility ought to cough up.
But the financial argument is much easier to make when propane is the fuel, at something like 3-4x the cost per BTU.
But lifecycle cost is usually way down the list the reasons why people go tankless. Item 1 is "endless hot water" (whether the reality lives up to the marketing fiction or not) and after that comes space-savings, etc.
I'm not a big fan of tankless HW heaters either, but I'm not against them.
There are very real differences between an LP and NG versions of the same model though- you need to buy the right version for the fuel used and set them up correctly, even if MOST of the components and sub-asseblies are identical. There are safety, efficiency, and heater-longevity issues that can be incurred from running it on the "wrong" fuel.