Ubuntu GNOME Remix 12.10 uses GNOME Packagekit ("Software") as the default package management application, but this will change in Raring Ringtail.
A recent update in Ubuntu GNOME 13.04 Raring Ringtail (currently under development) has removed GNOME Packagekit from the default applications, replacing it with Ubuntu Software Center and Ubuntu's Update Manager.
According to a post on a mailing list by Jeremy Bicha, the main Ubuntu GNOME developer, GNOME Packagekit is currently "pretty disappointing", while Ubuntu Software Center is "one of Ubuntu's best features with ratings and reviews, screenshots, app icons, access to commercial software, and decent search", so even though this change will slightly affect the pure GNOME3 desktop experience that Ubuntu GNOME Remix is trying to achieve, it will definitely provide a better overall default experience.
Further more, this won't be the first GNOME distribution that ships with its own software management application: Mageia and openSUSE do this too.
Also, as you probably know, Ubuntu GNOME Remix 12.10 includes the classic session by default (along with GNOME Shell, which is the default session, obviously). Well, the same 13.04 update brought another pretty major change: even though Ubuntu 13.04 is likely to ship with GNOME 3.6 for the most part, and not 3.8 (which will remove the fallback session), the classic (fallback) session packages were removed from the default Ubuntu GNOME Remix 13.04 Raring Ringtail installation.