According to packages.ubuntu.com, the version of GDM is 3.04.
For 12.04, most, but not all of Gnome 3.4 is available. Where there were clashes with existing (mostly) canonical supported packages, not all of the gnome 3.4 packages were made available in the repositories.
At the recent UDS, there was some consensus to attempt to get the vast majority of gnome 3.6 into the repositories. Thus gnome-shell users will get "a better experience".
Until then, you will need to stay with v3.04 GDM unless you use a third-party PPA such as described in the linked question. This will give you a similar login screen.
- How to get GNOME 3.2 login manager installed?