Update 2013:
All major repo hosting services supports git, and supports smart https access (see below):
- code.google.com (with cases like this one, July 2011)
- bitbucket.org
- tfs.visualstudio.com (!, as explained by Scott Hanselman)
Currently (July 2013), the main difference (between GitHub and other services) is in term of release management, more specifically:
- integration with Travis CI (continuous integration, possible more or less with all services)
- release artifacts: See "GitHub Release Your Software (July, 2d 2013)":
The ability to associate to a tag up to 100MB of binaries.
Initial answer (September 2010)
One big difference is the support by GitHub for smart http, as explained in the ProGit "smart http" section, supported since April 2010.

Being behind a firewall at work, that is more than useful to actually push anything to the remote repo!
I don't think "Google Code" support it officially, even though some contributors try to push that feature.