BF4 can have 4xMSAA on PS4 and none on Xbox One for example and they both could run at 1080p & 60FPS. AA is very taxing. Most people wouldn't even notice that much of a difference. They could could also turn off things like VSync on the One. Its easy to get the Xbox One to play games at the same resolution and FPS. There is not much of a difference between a 7770 and a 7850. I can barely tell a difference between me running Crysis 3 on medium and high settings. Both look phenomenal.
I don't think we will be able to notice much of a graphical difference even with the PS4 being more powerful. Especially not at first, all the devs for the PS4 were probably developing from the 4GB dev kits, so none of the games will really be fully optimized for the PS4's 8GB of ram. I've never really seen much of a difference between something like high and medium PC settings. The only real difference I can feel is frame rate, if the Xbox struggles with frame rate on the extremely demanding graphical games I would be very disappointed. I don't think that will happen though as they would likely just tweak some settings to ease the load.