This article, Google Analytics script, has a comment thread where people debate whether Google Analytics or WordPress.com Stats is better. The consensus seems to be that you might as well use both and that though Google Analytics has more info it might be overkill.
WordPress.com Stats was easy enough to install and I could use the same WordPress.com API key for all my blogs. The only issue was that to see the stats in my dashboard I had to enable third-party cookies in my browser (normally I don’t to keep out unwanted cookies).
Google Analytics took a little longer to set up but was still easy. I had to create separate Google Analytics accounts for each of my blogs. Google asked if I wanted to share my data and though I was suspicious I said yes because they said I would have access to other services if I did. I then configured the plugin for each blog with the correct Analytics Account ID. For this blog the footer does not call wp_footer(); for some reason so I placed the tracking script in the header. For my professional blog I placed the tracking script in the footer since that is the default.
I have a feeling I am going to end up liking WordPress.com stats better because it is simpler and more tuned to the stats I want from a blog. Below is a sample screenshot.
But I am glad I am also at the same time compiling stats on Google Analytics.