Irvine will undoubtedly be big dog in OC and will probably be well respected in the LA market as it is in the UC-system.
Even with their star faculty, that's still a huge if. The fact of the matter is that they're offering a full ride to the incoming class because they realize what a gamble it is to attend a brand new law school. You may be right that it will one day surpass UC Davis, but there's no way to tell now.
Keep in mind that New York and SoCal are EXTREMELY different. Cardozo is an excellent regional school, and you'll have fewer job opportunities available back West if you attend. On top of that, while Cardozo places decently, it's in a saturated market that is currently hemmoraging jobs. It's still really hard to argue with a full ride, though.
In your case, I'd probably pick either one of the full rides depending on where I wanted to work after graduation. GW is a cut above, but as you said you'll be paying significantly more, and you may find yourself stuck in D.C. for awhile after graduating (which is not really a bad problem to have).