I am familiar with other Stack Exchange sites that are out of beta and don't see a lot of difference. I think we get more elected moderators and they get special spam fighting powers and a cape but aside from that what changes....
This is only a partial answer, but as I see it, the changes that come with graduation mostly benefit a site with high activity levels, and dealing with high volumes of material. As we are, many of the changes would not even be beneficial. And as we are, graduation is not going to happen. We would need marked advances in activity.
From the link that Niall gave this comment from D.W. does not quote a source but it is thought provoking:
I'd like to add one more feature to your list. Today, sites in beta can be shut down at any time, and all their content disappears (well, there's an export, but it won't show up in search). For graduated sites, there's an implicit promise that this won't happen: Stack Exchange will continue hosting the archive of questions & answers. For me, I buy into the mission of SE as building an archive of high-quality content. If there's a significant risk that all my contributions might disappear at any time, that's a deterrent to contributing; knowing that won't happen would be a nice benefit