Rankings are retarded? Really? Then surely you can tell me why they still are so important. Rankings indicate prestige - this is a fact. It doesn't encompass the entire prestige of a school, but it certainly is a huge factor.
As far as your contention that median LSAT/GPA are the same for GW and Vanderbilt, this is slightly misleading. It's like saying oh well gosh, Georgetown and Chicago are virtually the same in terms of median GPA and LSAT, so they are peer schools. In fact, the percentile difference between Chicago (171 - 98th) and Georgetown (169 - 97th) is the same as Vanderbilt and George Washington's (166/94 vs. 165/93).
But I don't think anyone would say that Georgetown and Chicago are necessarily peer schools. In some ways, perhaps, they are. But there is definitely a reason why Chicago consistently ranks in the top half of the T14 and why Georgetown consistently is the reason the T14 exists in the first place.
The same thing goes with Vanderbilt and George Washington. They are peer schools in many respects, definitely. In terms of the quality of the faculty, probably very similar. The students probably are not the same quality - remember that a good portion of the GW class is part-time. Also remember that GW is the "second-best law school in D.C.," a burden which it has to constantly shoulder. It has been increasing in prestige in recent years, but it has not been a solid, historically prestigious school with deep connections to firms and power players. Someday perhaps.
why you think PT composition and "2nd best" has any bearing on the quality of student is beyond me
like i said, employers look to the #ers
and though you may think that a 166 is significantly superior to a 165, you are more or less alone in that capacity as most people, at least those in a position of hiring power, are familiar with the concept of stnd deviation and know that exact #ers are only really predictive of ranges
as far as your GT / UChi comparison goes, sure - the incoming classes are more or less equal is most relevant capacities and yet there is a difference in the ranking - but what does this really mean? in terms of employability, close to nothing. a GT grad is more or less on equal footing in terms of biglaw placement as a UChi grad - regional preferences aside. sure, UChi might have a more "academic" focus and thus places more into academica, but that is more of an institutional element as opposed to some sort of indicia of quality. those who want to teach go to certain institutions...the quality of the institution is really defined by the quality of the incoming students.
basically Vandy, GW, USC, BC, BU, UMinn, W&L, WUSTL, ND, Fordham, Emory and maybe W&M are basically the exact same school in terms of employment opportunities upon graduation - if you don't believe me go to nalp.org and research firms and where they conduct their OCIs...