Are we seriously comparing FFXIII to Uncharted 3 now? Are we seriously questioning the reasons one might want to play a JRPG over a TPS/FPS? Are we seriously questioning whether there is any difference between the two experiences that one person might enjoy more than another?

Because xD if that's the case.

You can't ask what makes a JRPG different to a WRPG and then take those differences and say "Then why not play an FPS game?" If I told you the differences between a JRPG and an FPS, you'd come back with "But why not play a WRPG?" and we could go in circles all day. Do you want me to tell you the reasons people might want to play a JRPG over watching a movie, too? And before you go "Well, actually..." - again, seriously...

Every genre has something that you could argue another genre has.

The key point of the genre is that it covers all or most of these varied differences from all the other collective genres.

JRPGs have a story, but that does not make them a Survival Horror.
JRPGs have a leveling process, but that does not make them a TBS.
JRPGs have dungeon areas, but that does not make them a Dungeon Crawler.
JRPGs have characters, but that does not make them a Platformer.
JRPGs can be 3D, but that does not make them a Space Trade & Combat Simulator.
JRPGs generally won't allow you to win every battle by pressing X repeatedly, but that doesn't make them a Fighter (Beat'em Up) game.
JRPGs characters have a personal tie to the overall plot, but that doesn't make them a Point & Click Game.
JRPGs characters generally have a fixed story to them, but that doesn't make them a FPS.
JRPGs generally have varying weapons with upgrade systems, but that doesn't make them a WRPG.
JRPGs can have multiple controllable characters, but that doesn't make them an RTS.
JRPGs generally have puzzles to be solved, but that doesn't make them a Puzzle game.
JRPGs generally have cinematics, but that doesn't make them a movie.
JRPGs can sometimes allow you to move characters around the field, but that doesn't make them a Sports game.
JRPGs generally do not require excellent hand-eye co-ordination with precise timing, but that doesn't make them a City Building Sim.

JRPGs generally have all of these things, or at least most of them.

So, to go back to WK's question of "what does FFXIII offer as an experience in relation to Uncharted, The Walking Dead, MGS4, or Heavy Rain?", I will simply say "it's a JRPG." If you want specific examples of why any one person might want to play FFXIII - a JRPG - instead of another game, you'll have to ask that specific person. I love Uncharted and I love Final Fantasy. I play them both. Honestly, I don't need a reason for this beyond the fact that I enjoy playing video games and they are both video games. But yeah, they're blatantly different kettles of fish.