My favorite story based FPS is Metroid Prime on the GCN, hands down!
First off, the setting was beautiful and varied. You had this lonesome atmosphere always pressing down on you, hard, in a good way though. The Metroid lore was so deeply explored and opened up by Retro Studios by taking the scan visor from Super Metroid and allowing it to tell large stories with little text. It made a simple shriekbat come to life with details on its living habits and other creature specific info. All of this was backed up by great gameplay and an engaging although simple story.
As for competitive FPS on the 360 I still love playing Halo Reach online in a team with my two brothers. Now if the thread will let me cheat on the question I actually prefer Gears 3 to Reach, but that's obviously 3rd person.
On PC I'd say Team Fortress 2, though I play Tribes Ascend a lot as well, and again if I could cheat I prefer Super Monday Night Combat to both of those. I prefer third person in general
