The nominees would have been different.
Hillary would probably have won if experience were more important to primary voters, as in the months after a financial crash. She might've made health care a bigger issue, if there was greater economic insecurity.
Romney would have done better if economic issues were much more important during those early primaries.
Bloomberg might have an opening if both parties are unpopular enough, although this wouldn't be the right candidates to run against.
As for policy, it might have been better for Republicans to have an extra year. Bush did get some credit for responding quickly to the economic catastrophe, so they would have gone for a major stimulus.
Romney's ties to Wall Street would have doomed him. I doubt he would have entered the race.
Actually, I think one Republican who would've done better, though he definitely still wouldn't win the nomination, is Ron Paul. His opposition to the Federal Reserve, TARP, etc. would get him some more traction. In the real timeline, he was mostly just known for his anti-war views, as that was the most salient issue at the time.
As for the extra year, that would've meant unemployment would peak right around the '08 election (if assume the same trajectory as IRL) and would clearly be on a downward trend at the time of the 2010 elections. It wouldn't be good for the GOP.
Nobody's addressing my point that other Democrats could attack Clinton for policies during her husband's presidency that led to the crisis.
