Titanfall is available on three different platforms and all the versions have differences, most notably in the graphics department. The Xbox One and PC titles look fairly similar (though the PC edges the new console), with the Xbox 360 understandably falling behind in terms of graphical fidelity.
Thanks to the guys at IGN, we now have a useful video comparing the graphics across all three versions, showing the game in motion and pausing to note the differences.
There's no question that the PC version on max settings looks the best, as is expected. I would imagine even on lower settings it still looks roughly as good as the Xbox One version, but they look pretty similar regardless. Everything in the PC version is mostly just sharper and clearer, especially textures. The PC can also pump out a higher resolution than the Xbox One edition, but all of this depends on the power of your rig, too.
The Xbox 360 does look decidedly last-gen in comparison, but it's still a good looking game. The lack of sharpness that the Xbox One version has compared to PC is magnified even further on Xbox 360, where you will definitely notice the largest differences. Fortunately, the game reportedly plays quite similarly compared to the other two, and retains most of the features as well.
One version of Titanfall that doesn't exactly hold up graphically is the playable Minecraft recreation, Ironfall. It does, however, keep most of Titanfall's features and mechanics too, even though it's just a modded server. Check out the comparison video below, and try Ironfall here if you have Minecraft.