The PS4 is more powerful but not as big of a difference as people think, and certainly will not have the impact in games people are expecting, especially with diminishing returns compared to PS2 vs Xbox era, we're talking a modern GPU with programmable shaders, hardware powered bump mapping and normal mapping, twice the available ram with greater speed yet we still saw games like God of War 2 that beat a lot of Xbox games.
When you compare PC games running on 1.2TF vs 1.8TF GPUs, the difference is basically defined by framerate while running the same exact effects and AA. In the case of PS4 vs X1, if BF4 is running 60fps on the PS4 while running 4xAA, you might find that the X1 version is also running 60fps but with just 2xAA and maybe a few tweaks to the shadow details to bring the framerate up to par, you'll literally need to compare these side by side in stills to point at the difference, which is cool for sites like Digital Foundry and to spark fanboy talk, but nothing significant that would make people choose one console over the other, the games should still be the number 1 reason for choosing, and looking at PS2 vs Xbox differences and as big as that was, the mainstream chose games. "Yooo, did you see Vice City? I want that game, gettin a PS2 cause Xbox doesn't have it" Just a 6 month exclusivity made that much of a difference, imagine what a year of Dude bro of Duty creators Titanfall could potentially do...
People expecting a drastic difference between PS4 and X1 are in for great disappointment.