Well the OP actually asked for the FPS with the most advanced graphics, so yeah I guess the other parts of a game engine aren't what we're discussing here. There aren't any GPL FPSs based on Ogre3D that I know of though...
Not out yet, but id tech 4 when it's released as GPL will probably be the most advanced.
I'd doubt that if you include unreleased engines. From the released ones... hm... difficult to say. Definitely though not Ogre since it is not a game engine just a render engine as mentioned above.
EDIT: Unreleased means here also not relased under GPL. Obviously Q4 is released under Windows but it is not released under Linux so it counts as unreleased under Linux.
Any idea when id tech 4 will be released as GPL?
Hmm, can't seem to edit my post.
Should have done some research first, from Wikipedia:
So not too long then, possibly...At the QuakeCon 2009, Carmack said that he planned to petition Zenimax to release the id Tech 4 source upon the release of Rage (expected in 2010).