Open world games suffer quite a bit from cross gen support. It mostly has to do with memeory. The xbox 360 only had half a gig of memory to work with, the ps3 had half a gig but split between video ram and system ram. Skyrim ran into save game issues on the ps3 due to low memory, for example.
No matter what technical tricks you do, memory is a hard limit to the amount of things that can be around in your game at any time. This is why alien isolation, a game that deals in small areas and enclosed spaces, was good on last gen hardware, as Johnny indicated. Shadow of Mordor, a much more open game, ran into severe issues.
Despite what people like Yahtzee say, the 7th-8th gen switch came at about the right time (perhaps a bit late) for a ton of technical reasons. They just don't jump out at you in the same way old hardware jumps did.
If Fallout 4 is cross gen it will have serious problems. Either the game will be limited to allow it to work on old hardware or the game simply we be bad on old hardware.