Clinton has said she is through with politics, but almost no Democrat believes that (including me). I might start to believe it if she's saying the same thing in January of 2015. As for Biden, he almost seemed to be campaigning already on inauguration day. He says he hasn't made any decision as to whether to run, but almost no Democrat believes that either.
What makes this such an interesting choice is that both are very popular within the party. Right now, Clinton has a lead. She almost won in 2008, and has served admirably as Secretary of State. Biden probably wasn't as well known four years ago, but he has also distinguished himself in service to the Obama administration and the Democratic Party in the last four years. I think most party members could happily support either one as their standard-bearer.
An ABC News/Washington Post Poll was conducted to see where the two stand right now. Here are their favorable/unfavorable ratings (with the favorable percentage being the first number and unfavorable being the second number):
HILLARY CLINTON
General Public...............67% - 26%
Democrats...............91% - 6%
Independents...............65% - 26%
Republicans...............37% - 57%
Men...............62% - 31%
Women...............72% - 21%
Whites...............63% - 33%
Blacks...............83% - 11%
Hispanics...............73% - 15%
JOE BIDEN
General Public...............48% - 37%
Democrats...............78% - 13%
Independents...............42% - 37%
Republicans...............20% - 71%
Men...............44% - 41%
Women...............52% - 33%
Whites...............44% - 46%
Blacks...............79% - 15%
Hispanics...............44% - 22%