The biggest facilitator of a different next-gen experience will be the SSDs.
Do you folks remember Far Cry 2? Do you remember the complaint that the vehicles were so slow? The vehicles were slow in Far Cry 2 because the game could not keep up with loading the world.
We can only speculate how that would impact other games. But if you look at a game like Days Gone, the bike is oddly slow in that game, and the game still has a lot of performance issues. Days Gone looks like it tries to mediate this issue with similar design to something like Destiny, wherein much of the world is cordoned off into smaller sections, giving each time to load as the player passes through.
Despite making the bike slow, and offering a relatively constrained open world setting, Days Gone still has issues with its performance, particularly as the bike becomes faster in the late-game areas.
On the PS5 those games could break free of those design limitations (hopefully). We could see faster and more realistic traversal in a title like Days Gone, with more realistic landscapes that didn't need to be stitched together in such an unnatural way.
If you're tied to old hardware, you can't change the game like that. You can make the game perform and look better, but you can't change the core design (e.g. the structure of the open world, or the speed of traversal). Which means that your titles are fundamentally being designed for old hardware.