Sometimes the current is important, which you may find useful to compare with the torque in a car as opposed to its power. In a car the torque is the pulling power, whereas power gives top speed - roughly speaking anyway!From online reviews of ATC speakers it is clear to me that there are some amps out there which may have output of 100 or even more watts into 8ohms compared to another amp driving the same ATC speakers with output of 80watts into 8ohms , and for some reason its the latter amp which drives the speakers a lot better than the former amp; so it implies to me that there is more than just simple Power Output having effect on the driving capabilities of an amp?
If a speaker drops to 4 ohms or less over quite a bit of its frequency range then a higher current amp will be better. It might measure 80 watts into 8 ohms but 160 watts into 4 ohms. A weedier rival might reach 100 watts into 8, but just 110 at 4.
ATCs aren’t very sensitive - loud, if you like - per watt, but they are a benign load, rarely dropping below 6 ohms. So they’re easy to drive, hence compatible widely, but prefer a bit of power to get them going optimally.