What difference will GTK3 support make for Emacs?

Function wise none (except it might be easier to use for people with disabilities) but esthetically it's a little bit better. I don't know of any drawbacks when it comes to GTK3.

http://batsov.com/articles/2011/08/19/a-peek-at-emacs24/ here is a good list of the new features.

Screenshot of Emacs 24 (GTK3):

Screenshot of Emacs 24 (GTK3)