Cython is now considering options where to move the main (mercurial) repository, and Robert Bradshaw (one of the main Cython developers) has asked me about my experience with regards to Google Code and GitHub, since we use both with SymPy.
Google Code is older, and it was the first service that provided free (virtually unlimited) number of projects that you could easily and immediately setup. At that time (4 years ago?) that was something unheard of. However, the GitHub guys in the meantime not only made this available too, but also implemented features, that (as far as I know) no one offers at all, in particular hosting your own pages at your own domain (but at GitHub's servers, some examples are sympy.org and docs.sympy.org), commenting on git branches and pull requests before the code gets merged in (I am 100% convinced that this is the right approach, as opposed to comment on the code after it gets in), allow to easily fork the repository and it has simply more social features, that the Google Code doesn't have.
I believe that managing an opensource project is mainly a social activity, and GitHub's social features really make so many things easier. From this point of view, GitHub is clearly the best choice today.
I think there is only one (but potentially big) problem with GitHub, that its issue tracker is very bad, compared to the Google Code one. For that reason (and also because we already use it), we keep our issues at Google Code with SymPy.
The above are the main things to consider. Now there are some little things to keep in mind, that I will briefly touch below: Google Code doesn't support git and blocks access from Cuba and other countries, when you want to change the front page, you need to be an admin, while at GitHub I simply add push access to all sympy developers, so anyone just pushes a patch to this repository: https://github.com/sympy/sympy.github.com, and it automatically appears on our front page (sympy.org), with Google Code we had to write long pages (in our docs) about how to send patches, with GitHub we just say, send us a pull request, and point to: http://help.github.com/pull-requests/. In other words, GitHub takes care of teaching people how to use git and figure out how to send patches, and we can concentrate on reviewing the patches and pushing them in.
Wikipages at github are maintained in git, and they provide the webfrontend to it as opensource, so there is no vendor lock-in. Anyone with github account can modify our wiki pages, while the Google Code pages can only be modified by people that I add to the Google Code project, which forced us to install mediawiki on my linode server (hosted at linode.com, which by the way is an excellent VPS hosting service, that I have been using for couple of years already and I can fully recommend it), and I had to manage it all the time, and now we are moving our pages to the github wiki, so that I have one less thing to worry about.
So as you can see, I, as admin, have less things to worry about, as github manages everything for me now, while with Google Code, I had to manage lots of things on my linodes.
One other thing to consider is that GitHub is only for git, but they also provide svn and hg access (both push and pull, they translate the repository automatically between git and svn/hg), I never really used it much, so I don't know how stable this is. As I wrote before, I think that git is the best tool now for maintaining a project, and I think that github is now the best choice to host it (except the issue tracker, where Google Code is better).