Google Chrome has several things Chromium doesn't.
1. Google Chrome has an optional program for reporting bugs and browsing habits. Many people don't like the idea of Google peeking in. Google Chrome also has an auto-updater so you always have the most recent version of the program, chromium does not.
2. Google says they "test" their versions extensively before releasing them to the general public. You don't necessarily know what kind of testing happens with open source builds of Chromium.
3. since the "Canary" build of Google Chrome, you can associate your Google Chrome with a google profile. I'm not sure if Chromium does that. I don't think it does.
4. You're forced to use the Google installer that downloads a downloader rather than downloading a huge all-in-one install. So, you can't really download Google Chrome then like, install it offline. Chromium packages it all in one.
5. Oh, if you really want to you can build your own Chromium. Change stuff, do your own Joe-Blow Browser. What fun.
Other than that, they run the same extensions, themes and plugins, you can get recent release candidates of each, they are very similar. Note that even though Safari is also based on webkit, Chromium and Google Chrome are much more advanced in development.