That is a really tough call. They are both such good schools. I would say it comes down to personal preference. Richmond's campus is GORGEOUS and doesn't really have an urban feel to it. American's campus, however, is urban. Which do you see yourself being happier in? If money is an issue, I would take Richmond definitely.
Im not sure what you mean about GMU nipping at its heals. GMU has been first tier and upwardly mobile rankings-wise for a few years now. American is a great school, but i think most would agree GMU is superior.