I think Hillary doesn't have the charisma of Obama.
Foreign policy would be much the same. I'm not so sure about Domestic policy.
Hillary would turn into a culture war warrior. Thus she would not pick needless fights in domestic policy regarding contraception orders and would also not initiate crude attempts to intrude in the internal governance of churches (
Mount Tabor, 9-0 loss for Obama).
As a side note, she would also recognize that a continuing series of addresses to school children by an elected leader are not in accordance with historical practice in the U.S. (there is nothing inherently wrong with the addresses either). Though the matter is small, Hullary would reject the addresses as unnecessarry and out of norm
Basically, I think Hillary would receive far more advice from Bill CLinton, a master politician, and would be more prone to follow it. She would face a far easier race in 2012.