Honestly, Secretary of State does more important work than the Vice President in American politics. Sure the VP is an extension of the President's policy and administration - offering some legal advice, too - the Secretary of State is actually in charge of conducting state diplomacy (President's still the boss, though). Biden was chosen to supplement one of the Obama ticket's perceived weaknesses, that being experience. Obama was a first term senator running against John McCain who had been around for decades. So Obama chose Biden, who had been around for decades as well.
It's hard to say if Obama would endorse his VP if his VP was running in 2016. Eisenhower's endorsement of his VP Richard Nixon in the 1960 election came considerably late; Nixon attributes much of his defeat in 1960 to a lack of support by Eisenhower. Objectively, Hillary Clinton is a career politician who likely would've declared her candidacy for presidency had she'd been VP. I don't see her campaign being run differently, however. She's already making an effort to form her image as Obama's third term.