Despite storage being the weakest link, I'm not concerned with next-gen storage speeds seeing what's possible with a streaming engine designed around a mere 20 M/s in Spider-Man on PS4. Next-gen has several order of magnitude improvements for data accessibility. They also have real CPU cores, so nothing should be anemic.
Most likely the only thing I'll be able to complain about is the OS/Dashboard UI if they use the current-gen designs -- every current-gen console has horrible UIs. Not a single one of them has it figured out -- Nintendo, Sony, Microsoft, Google, Valve.
+1 in the Spiderman GDC they explain how they load people on the ground only when you get near ground because of the streaming, it means the GPU can display something but it is not done because the streaming system can't keep up. It will never be the case.
For UI at least it will be fast. It is nearly impossible to come back to HDD after working with a PC with an SSD.