Biden was not from the opposite camp as he never endorsed Clinton in the primary. He got fewer votes in the Iowa caucus than Sarah Palin got for mayor of Wasilla. If Obama had true balls he would have picked Hillary.
Biden picked someone who'd be loyal, and was unquestionably competent. Had he picked Hillary Clinton, he'd have picked someone who doesn't know the meaning of loyalty. She's all about herself, and she'd have been finding opportunities to upstage Obama at Obama's expense, or instances where backchannel criticism would get out about how Obama should have acted differently, etc. That's a wise choice. Disloyal subordinates undermine any enterprise. Hillary caused enough problems where she was. There wouldn't have been a Benghazi, or a President Trump, if Hillary had remained the Senator from NY.