McCain picks Sarah Palin

The issues she's had to deal with are completely different from the issues a US president has to deal with.

As are any issues any member of the Senate has had to deal with. The difference here being that being governor gives a taste of the executive branch, while being in the senate puts you at the top of the legislative branch. Totally different things... Might as well say being in the Senate would make you a good Justice in the Supreme Court, or being President would make you more apt to be a Justice. It makes no sense to make this claim, and this is on top of the fact that NOTHING can give the experience that will make a good President.

I also don't think that Palin and Biden are very analogous.

The analogue is:

Obama <-> Palin
Biden <-> McCain

Obama and Palin are both young and have relatively very little time in government. Biden and McCain are old and have plenty of time in government. That's how they connect.