I expect some cool cutscenes, but nothing lengthy, just each character with their own 20-or-so minute arcade story. They announced that the original writer of Bioshock is writing Big Daddy's story, which is AWESOME!
To be clear, there really isnt a story mode per se, just an arcade mode with a loose story stuck in there. There isnt a Smash Bros type Adventure Mode, which is a massive shame imo.
In the sequel, they better have a Smash Bros style story.
I wanna see Sephioth pilot a metal gear, dammit.