Are you going for a JD or a Master's? Assuming you meant JD, I think the decision comes down to money and location. Both are good schools, both will offer almost identical educations (as will most law schools), and both will provide post-grad job opportunities that are mostly within their respective regions.
In other words, if you want to live in DC go for GW, and if you want to live in St. Louis go for Washington U. I don't know about the job prospects in St. Louis, but Wash U is the big dog in town so that's going to help. DC is a very competitive market, but the job market is much larger. Keep in mind that outside of their regions, each school will be viewed very similarly.
Has either school offered any money? That's a huge factor.