The ruling issue is standby heat losses.
For instance, our water heater at the lodge is on a timer. 36 hours after the timer ran out, I had occasion to check it. It was tepid. So that means it fell from 60°C to 30°C in 36 hours, or 0.8°C per hour.
*Except remember: thermal losses are proportional to the difference in temperature, and ambient was 25C. So, skipping a bunch of math, let's just say our losses at operating temperature were 1°C/hr. (closer to 1.75°C according to comments below).
That 30 gallon tank is about 120 kg, so that means we were wasting 4180 J/deg/kg x 120kg x 1°/hr.
Multiply All that and cancel the units and we get 501,600 joules/hour. Or 139 joules/second, which is watts. (or by the other math, more like 850,000 j/hr or over 200 j/s=watts).
The difference is that (our roached old) heater wastes 139 watts when it is in standby. That makes sense; that is simply a matter of insulation losses. A tankless heater would waste 0 watts while in standby.
Our rule of thumb is that a 1-watt load costs 1 USD per year. Probably works for Euros and quid, too. So about $139/yr or about $12/mo. (by the better math: over $200).
Another factor: Piping distance
There will be some length of piping between the water heater and the spigot. After some minutes of disuse, the water in that pipe will have cooled down to ambient. So the common practice is to flow the hot water valve until the water actually warms up, then set to your shower, washing, whatever. When one is finished, one abandons the hot water in the pipe. This cools down within minutes even if insulated. This is a total energy loss. Worse if someone enlarged the pipes for better flow, since more volume of water is abandoned.
This problem invites a wasteful workaround: "recirculation systems" which pre-load the pipes with hot water. That means fast hot water but it also means much greater heat losses.
What does this have to do with the tankless question? Real simple: Electric tankless units are very compact and do not have flues - which means they can fit in all sorts of places a 30-gallon tank would not. That means the tankless(es) can be moved much closer to the points-of-use, and that means less abandoned water and more convenience. At extremes, the British put their "electric shower" heaters right at the showerhead - and those units only take 8500-10,500 watts (35-45 amps).