I know people will get on me about my Joementum stuff but Biden really would be Obama's best choice. Obama's main weakness is his perception as inexperienced and who better to pick than a Senator of over thirty years to balance that out?
With his 35 years worth of experience, I think he would end up overshadowing Obama. I think he would be better off as Secretary of State.
But experience is what he needs on the ticket. It is like how in 1960 Kennedy balanced his ticket by getting someone with years of experience(Johnson)