How to upgrade two different versions of WP?

Hi everyone,
Here’s my situation:
I have an existing blog on WP 2.0.4, and I’ve been working on a new version of the blog on my desktop using XAMPP and WP 2.1.

I find 2.1 to be a little buggy, so I want to upgrade to 2.3.

I was wondering what’s the best way to go about upgrading to 2.3 and then deploying.

I was thinking I would upgrade the live blog from 2.0 to 2.3, and then also upgrade the XAMPP blog from from 2.1 to 2.3. That way the databases should be the same, right? And then I can simply copy the theme over from my XAMPP blog to the live blog.

Will that work?

Thanks for any tips!