Apple did the same again with their ARM migration and in my experience it worked great. I believe Microsoft also has a solution for running x86 software on ARM.
The original Rosetta, which was emulating PPC on x86 is directly comparable to the situation of PS3-game-on-PS4 hardware. I was able to play Halo CE for Mac on x86 with Rosetta and it felt native.
The point is that this isn't a limitation of technology, this was a decision on Sony's part.
There's some weird online connection issues on 360 that occur with certain modern routers. You get dropped randomly from the game. Annoyingly, the emulated 360 on One doesn't skirt around the issue. It was annoying for Borderlands but made Left 4 Dead worthless on anything besides easy