There are graduates of both programs on this site who will probably chime in at some point, but yes both are highly competitive/have great residents/rock star faculty. If you want a research career most people would say Yale simply because they have produced more department chairs and national figures than any other program (John Krystal, Dennis Charney, Eric Nestler, Chris McDougle, Wayne Goodman, Mark Gold... the list goes on.) BUT you really won't lose anything if you pick UW. Some people on the west coast might even say that UW is better
Agree with OPD- the real question is do you want to live in CT and get taxed like crazy because all of the super rich people have their assets in things that aren't taxed/hire accounts to find obscure loopholes hence the current budget crisis... or do you want to live in Seattle- where you have the largest influx of people in the country driving up real estate prices and a minimum wage law that has basically made the hole in the wall type restaurants and small businesses defunct. (in reality both places are great, what I just said notwithstanding)
The original poster was asking about University of Washington in Seattle, not Wash U