Hrm.
Well, Texas is ranked higher, which translates into a greater degree of national portability.
I'm partial to DC, myself, but I'm biased -- I grew up in this area and I love GW (current 2L). We do have a LOT of offerings in National Security, plus you really can't beat the area for internship/externship opportunities -- the appellate court for Gitmo's military trials is down the street, as are all of the military courts of criminal appeals, DOJ, the immigration court, and the Eastern District of Virginia's rocket docket. While interning at those places is hella competitive over the summer, because of our location you can extern there for credit during the school year. So there's that.
Housing for a family of four in the DC area is fairly expensive, depending on how far you're willing to live from the city. You can find some affordable places in the suburbs in Maryland and Virginia (I live in a four-bedroom in Woodbridge, which set us back $390,000). The commute isn't bad either -- I generally drive in with my dad and have my husband pick me up after school, but if you live near a metro station or near the VRE (Virginia) or MARC (Maryland) trains, that's another option.
I don't think you can lose with either choice, really. UT has the higher ranking to consider, but GW has some great geographical bonuses. If you're free-riding it at both schools, this is pretty much a champagne problem.

Good luck with your decision!