There are **two** ways that a decrease in attack speed influences active attacks. Not only is their animation speed relevant, but also their cooldown because it influence the active attack/noactive attack ratio.
Imagine an active ability that takes 1.5 second, with a 10 second cooldown. and regular attacks taking 1 second.
So in 100 seconds, you get 10 active attack (15s). And 85 regular attacks. Now say the active attack has +100% dmg, for simplicity. So that is '105' damage in 100 seconds.
Now there are three "10% slower" scenarios imaginable:
1. active attacks don't get slower but regular attacks do (this is NOT the case for many active attacks). Were that the case, you get 10 active attacks (15s) and 77.3 (85s) regular attacks . That results in 97.3 'damage' in 100 seconds.
2. active attacks do also get slower (as far as I know how many active attacks work). You get 10 active attacks (16.5s) and 75.9 (83.5s) regular attacks . That results in 95.9 'damage' in 100 seconds.
3. active attacks do also get slower *and their cooldown is increased by 10% to 11 seconds* (this will NOT be the case). Would this be the case, you'd get 9.1 active attacks (15s) and 77.3 (85s) regular attacks. That results in 95.5 'damage' in 100 seconds. now **this would be the only true 10% dps loss**.
Maybe people are pointing out the difference between 1 and 3. And you point out the slower animation speed, so the difference between 1 and 2, which although true is not complete. there is still a difference between 2 and 3, so an attack speed reduction and equal damage increase does indeed favor active attacks (that are worth it, dps-wise) slightly.
(for those good at math who have spotted the difference between 10% slower and 10% longer animation, read all this with 11.11% slower in mind but it's symmetrical in all scenarios, the point is that because of cooldowns a slower attack speed and more damage is actually slightly favorable)