We can cut this issue so many ways. Objectively, there isn't much to distinguish Obama's experience from Palin's in a way that produces a clear advantage with one exception that I'll get to later.
On Obama's side of the scale, Illinois is bigger than Alaska and, at least for us who live in places that are more like the former than the latter, more sophisticated. On Palin's side, she has executive experience - something that, as Jim Lindgren points out - requires dealing with scarcity and choosing between less than ideal alternatives as legislative experience does not - or, more accurately, permits these realities to be ignored. In addition, Palin can point to more things that she has done with that experience. She took on a corrupt state establishment, while Obama made peace with the Chicago machine. She made difficult choices about spending while Obama blithely supported more of it in a state that already faced a budgetary shortfall.
Part of the problem for Obama stems from the fact that he has almost had his eye on the next thing. In National Review, x reports that he has spent an astonishing 59 out of the past 112 months running for office. That he has done little in the Unites States Senate is not surprising. He has been running for President since he got there.
But there is also a sort of redemption for Obama in this. He has run a very good campaign for President and that's an accomplishment. Voters have gotten an opportunity to see him on the national scene and enough were satisfied for him to win the Democratic nomination. In this, he has an edge over Palin.
Now how much that matters is another question. He's not running for Vice President.
But, more fundamentally, the same opportunity for validation is open to Governor Palin as well. Whether - in November - she is seen as an acceptable candidate for the Vice Presidency will turn on how well she does on the national stage. People want to compare here to Geraldine Ferraro and Dan Quayle. Ferraro, with the exception of her husband's unsavory connection, was not a particularily bad candidate. Mondale's task was hopeless in '84.
Quayle was a bad candidate who suffered from being thrust into the national spotlight before he was ready, although Bush 41 still won.
The point is that Palin will make her own case in the next few months. If she can do that, then no amount of sexist allusions to beauty queens and dismissive snorts about Wasillia and Alaska (remember Plains and Arkansas?) will matter.