I'd give a slight edge to Republicans.
Parties always lose support after enough time in the White House. Hillary will not be able to distance herself from an increasingly unpopular President Obama. Her decades in public life mean she has a fairly high floor, but that she is also a poor agent for change. Demographic trends favor Democrats in the long term, but not quickly enough to have an impact here.
She's likely to be the Democrat's McCain, a respected figure who polled well initially, but got the nomination in the wrong cycle.
The big unknown is the significance of the first female President. We just don't know if there are enough Republicans or conservative-leaning independents who believe that milestone is worth a third term of Democrats in the White House.
Despite Obama's current unpopularity, I'm sure it's going to be more like 1988. Hillary will probably win, but she'll be defeated in 2020 by a moderate republican.