It isn't exactly clear to me why you would take Tulane out of the equation. They have a great M.Arch program, with the students getting very involved in rebuilding New Orleans. Many have actually gotten to see their work built, and worked with students from the business school and other disciplines on helping local businesses and others.
As far as academic quality, the students at Tulane have virtually the same stats as those at UVa. Compare the common data sets (Section C) of the two schools. As far as % admitted go, it is impossible to compare a private school with a state one, regardless of application cost. The inherent pool of applicants is too skewed in the case of a state school, not to mention the state requirements limiting the % of OOS, to make these comparisons meaningful. Add to that the different marketing approaches of schools, public or private, and the statistic gets less meaningful yet. It only really helps if you could see the % admitted with a resume similar to yours, and that is not possible.
Anyway, Tulane has a great program and a very nice campus in a unique city. Go visit. Give it some more thought.