Moving from modern street GT3 to 996 Cup is relatively easy transition. The lower weight of the Cup is offset by less HP (370-390 vs 435-450) so absolute speed difference is not that great. 996 Cups have standard manual transmission and ABS providing a level of forgiveness not found in 997 Cup.
What you notice initially: noise and immediacy of controls creates much higher sensory load. Suspension is considerably stiffer which translates to much less vertical motion. Assuming you're running slicks, slip angles are lower and threshold between sliding and breakaway is much narrower. Cornering limits/speeds are ultimately higher...once you get there. Major difference between learning to drive it and learning to drive it fast. Can't speak to the latter.
Re: 997 Cup, can only speak from the right-hand seat, but the big difference is the sequential box, which ratchets the intensity level up a healthy couple of notches. Lack of ABS demands higher level of braking skill...so I'm told. And it's a healthy chunk faster.