Well.. but a gas boiler keeps a 100-liter tank at temperature 24 hours a day plus reheating the withdrawn water... A tankless water heater maybe heats 60 liters during half an hour a day...
Reheating costs just as much energy with a tankless system as with the tank. The only difference is therefore the amount of energy the tank uses to maintain temperature. Our tank here loses under 5 degrees in 24 hours, which means for me about 15% of the energy (this also matches the heat energy loss specification from the manufacturer). With gas boilers, the energy costs only about a quarter, so you can keep the water warm for 300/15=20 days at the same cost as an electric tankless water heater (400% energy amount, minus 100% to heat up and per day 15% to maintain temperature). I hope that was enough calculation to follow, for more numbers I need more input. Putputput.
Otherwise, one should note that gas boilers also do not have their highest efficiency immediately after starting up, but first have to "warm up" (simply put, for example, the heat exchangers inside need to be heated, etc.). Therefore, it is additionally more efficient to load a tank than, for example, to fire briefly just to wash hands. That would at least argue in favor of a small tank when considering gas tankless vs gas with tank.
Likewise, of course, an electric tankless water heater also has a lower efficiency, especially with many small volumes of water.
from the road