Interesting thought experiment from Slate's Double X. Emily Bazelon says that much would have been the same substantively, but:
One specific counter-prediction: If Hillary were president, we'd either have more troops on the way to Afghanistan by now or we wouldn't. She wouldn't have taken her time to ruminate the way Obama is doing, because the barbs about weakness and dithering would have sunk in deeper.
I think we almost surely would have more troops on the way. I don't think dithering would have been the issue for Hillary so much as the fact that her instincts are simply more hawkish than Obama's, something I wrote about at length in early 2007, and I like to think the piece holds up. We don't know a whole lot of detail about what Hillary has been counseling in the Situation Room this fall but it sounds like she's leaning towards substantially more troops.
I can think of two other differences likely differences. One, I suspect we'd simply be seeing a lot less of a president Hillary--fewer grand speeches and TV appearances. The presidency would likely seem a little smaller, a little more modest. (That's not a knock on Obama; when you've got star power like that, you may as well leverage it.)
I also have to wonder whether a Clinton II administration would have started out by squeezing Israel over settlements, although it's not as though Hillary has dissented from that line, so who knows.