I've only played as Bahamut so far, but I've seen people use the other girl (non-DLC) and then also Sayuri (DLC).  Sayuri doesn't have guns and only uses a sword to attack, holding it down I guess gives her a projectile as well.  Is Sayuri the only character that plays different?  Or do all the characters have other variations to them like jump height or something.  I'd like to try the others out but I'm hooked on leveling up Bahamut.

lol I didn't even know Sayuri could charge her sword. I guess turbo isn't always the best :p
 
I'd like to know the difference between Krystal and Bahamut. There's gotta be a difference since she starts with less health and in arcade mode that doesn't make a lot of sense.

My buddy used Harley and had four hit points.  Didn't notice much of a difference besides that, except that he had some different unlocks available.  I had Speed Queen for Krystal, and he had something about toughness instead.
 
And Krystal vs. Bahamut, I think there's a minimal speed difference.  I think.

bahumut starts with the vault action chip while Krystal has the infinitely less useful ambush skill, i think there is some speed differences but for mw its unnoticable, i havn't tried any DLC characters yet.

Currently playing through arcade mode with  Sayuri her sword own bosses makes the game alot easyier in coop if the other person has a gun

From what I noticed, Bahamut has a 3 hit points while Krystal just has 2.  Both Bahamut and Krystal and vault over boxes.  I think Bahamut moves slower.  And one significant difference is that Krystal can deflect bullets back to the enemy.