Internally, I hope they keep all the same stuff; ideally, there's no need for the PS5 to care whether you're using a DS4 or 5.
Biggest complaint I have is battery - make it accept AAs, so I can always switch out my own rechargeables. The PS4 and 3's internal charge cycles are going to get really annoying after not too long.
The other thing I really want to see is a revised aesthetic. Nice as the DS4 feels, it looks bad imo. Give some kind of sculpt to the totally round handles, give it a nicer silhouette, or something. Not sure exactly, and it's such a small part of the experience, but I'd like it to be nice to look at.
Both sets of shoulder buttons could certainly feel better too I guess. The bumpers and triggers on the Switch Pro are good, and the triggers from the 360 and One would all be good examples to go from.
I think it'd be neat if the touchpad become a touchscreen. But I also think the downsides to that would outweigh the benefit. Quicker battery drain, more expensive controllers. It goes against my first point too, in that DS4s would no longer be exactly as capable.