Full disclosure, AU is my alma mater, so I am biased, but...
When people say AU is considered a lesser school than GWU, I feel the need to point out that GWU doesn't have an edge in terms of employment outcomes in the city, at least last I checked. Employers in DC have great respect for students coming out of AU's programs and the School of Public Affairs staff do a great job of supporting their students and connecting them with opportunities from what I've seen.
As an undergrad at AU, found that I connected better with the students there than at GWU, where I spent a decent amount of time as well. The fact that AU offers more aid opens the student body up to a little more diversity of backgrounds. I found there to be less of a sense of entitlement at AU. That being said, it's probably arguable that GWU has more name recognition outside of the DMV area.