As aforementioned, her foreign policy is likely more old-fashioned. For example, in 2008, she made it clear she would follow the advice of the Pentagon before beginning a withdrawal from Afghanistan and Iraq. There is probably no Rapprochement with Iran and Cuba, leaving Guantanamo Bay still open.
On Domestic policy, she probably does better when it comes to economic recovery, especially because her husband, being a former president could give her plenty of advice. I think she'd be a little more ambitious when it came to universal healthcare and education, because of how vocal she was about these issues as First Lady. Drug policy/criminal justice reform, she likely takes her husband's conservative route. Immigration, gun control, and LGBTQIA rights are where I find her to be similar to Obama, in order to court voters of those groups (although she may be initially reluctant when it comes to LGBTQIA issues, given her speech to the Senate in 2003). How she responds to racial issues is completely in the dark for me, although, after a hard-fought primary season against Obama, she likely takes the same approach and makes friendly with them.
I think she'd win against Mitt Romney in 2012 without a sweat, especially with Tea Party-esque conservatives dividing the Republican Party (some reactionary conservative group will arise in the wake of a second Clinton presidency). Romney, having to pander to that audience, will drift to the right and make himself out to be a corporatist-capitalist vulture/robber baron. Which will play into the Democrats' hand of tying him with CEOs that played a part in the 2008 economic collapse and easily associating him with the Bush-Cheney Administration, especially after their endorsement of him.