Thanks for your responses. I am interested in them both for their mathematical biology research -- the trade off, in my mind, being one of location vs prestige.
Being an international student may make visiting somewhat difficult although yes, it does seem necessary to make an informed decision.
My own feeling is that Cornell's maths dept is held in very high regard, 'clearly above' UW's maths dept -- and as Kaz says, somewhat comparable to Harvard, Caltech and MIT. However, how the applied maths depts compare I am less clear.
How do you find living in 'isolated' Ithaca?