One strange, but cool thing I noticed with the Vita version - I have the PS3 version via PS+, but I never bought any of the DLC, including the Mechromancer pack. The Vita version comes with the two DLC classes, one of the level cap increases, and two of the DLC campaigns, but that only works on the Vita, they don't transfer back to the PS3 version.
I started a new Mechromancer, since I really like that character, and decided to try cross-saving it over to the PS3, figuring it would probably tell me I'm not allowed to play her because I don't own the Mechromancer pack there. Surprisingly, it actually did let me load my save file and keep playing her, although it reset her appearance to stock because I don't have the costume pieces unlocked, as I don't actually own her on the PS3. I can't start a new Mechromancer or Psycho on the PS3, but the PS3 is fine playing the cross-saved file from the Vita. Weird, but pretty cool.