If Barack Obama had picked Hilary Clinton to run as his Vice President, he would have won by an even larger margin than he did. Hilary Clinton almost beat him in the primary, and in many polls, she is much more popular than he is. So yes, he absolutely would have.
I'm not a huge fan of Joe Biden, but I suppose he does his job. At least he isn't out shooting people on the weekend. Had Barack Obama run with Hillary Clinton in 2008, I would have still voted for him. I think this election was determined by the bad choice of the Republican Party, not so much Obama himself.
Having Oprah's approval certainly helped a great deal, but what won the election for Obama was the ideas he had to help the country. That is really what wins the election. There were a lot of strange rumors around him, but in the end, the running partner is just a formality.
It was difficult enough selling the first mixed race president. Pairing him with a classic white guy made it a little more palatable for those who still hold racial prejudices. Hillary Clinton is a powerful politician and has served the Obama administration well in her current position. However, pairing her with Obama is too far from the white man/white man combo of president and vice president. in the US for bigots to accept.