So I installed Ubuntu GNOME 14.04 (which included GNOME 3.10) and noticed that GNOME Software Center isn't included and isn't available through the repositories. Then I tried installing Ubuntu 14.10 (which included GNOME 3.12 stack) and, you guessed it, no GNOME Software center. Only the Ubuntu Software center.
Any idea why the devs didn't include it even as an option? Isn't Ubuntu GNOME meant to be a vanilla-GNOME-type-of-distro?
I would say it's because Ubuntu has it's own Software Center which is better then GNOME Software Center, in their opinion. Ubuntu GNOME FAQ says the following about it:
Source: http://ubuntugnome.org/documentation/faq/
But I'm pretty sure there is a possibility to install it, even though I can't tell you how.
Gnome SOftware Center will now be available on 16.04 release to replace the current software center. So probably you can install it now.