Maybe I am too old, but I hardly feel any differene.
I am not saying it is not there, I am saying I cannot feel it.
The only difference is in the triggers, where you have to press more or less on the PS5.
As far as the haptics go, the degree to which cross-platform games use them really varies. Cold War had cool haptic triggers so you felt the recoil kick, but I don't think that was included in MW2. Some exclusives like Returnal leverage the advanced haptics in a really impressive way, too, but I don't think we'll see that in many cross platform titles.
It takes a little getting used to, and there’s a good number of settings parameters you can dial in to your preference (I generally like higher sensitivity and on all the time), but now I’m able to snipe across the map with a controller in fortnite nearly as well as I used to with a mouse and keyboard in battlefield 4. Playing it on an Xbox feels like using stone tools in comparison.