The consoles are clearly using a lot of FXAA. This technique gets rid of aliasing for almost no performance penalty, but creates a tremendous blur effect that gets rid of details. Not just on the edges - but on ALL textures does FXAA ruin the imagine.
Take a look again at the comparison. Note the wall textures coming from the left (the one not in the foreground). The detail on the PC version is much larger because it is using proper AA.
http://www.neogaf.com/forum/showpost.php?p=176542201&postcount=1258
What's sad is that even using performance negligible FX AA, they still cannot achieve 60fps. Even if the poor CPU speed is why they are stuck at 30fps, there is no excuse not to use proper AA. Again, my laptop PC GPU is pretty comparable to the Xbone and markedly slower than the PS4's yet was able to custom edit the config to get higher AA - and not FXAA. In their porting efforts, they must have determined that using proper AA would require time to figure out, so they took the easy way out and smeared what I like to call FauX AA all over the screen. Laziness or lack of monetary incentive, but they didn't even try.