I voted Binary Domain since I think it's the best of the three. However, Dead Island does have a sequel coming out soon-ish and you can import your old Dead Island character, with all his levels and such intact, into the new game. Don't think Dead Island has split-screen, though, only Online and LAN co-op.
Vanquish is alright, but to me it just seems a bit too "arcadey" for my tastes. You can probably find it somewhere for dirt-cheap though, if you really want to pick it up. I frequently see a few copies floating around the cheap bins at Wal-Mart for maybe $10-$20.
It's a tough call between Vanquish and Binary Domain....They both rank as two of my favorite games this gen! I'd give the slight edge to Vanquish, but they are two completely different games that both deserve to be played.
Best of 2012: Sleeping Dogs, Mass Effect 3, Max Payne 3, Far Cry 3 Gamercard: http://card.psnprofiles.com/1/Carib2g.png
Can't really go wrong witht he first two choices. I got bored with Dead Island. And really it's just a loot game and if that was something that interested you I would point you to Borderlands 2 which is supieror in every way.