which is the best and why?
I'll do my best to try and answer this question with some modicum of intelligence. Curtis is a throw-back school, you can just feel it when you enter the building (it's actually an old house). It's a preserver of tradition, old and steeped in lore. Curtis is much, much smaller than Juilliard (for example there as nearly as many piano professors at Juilliard as there are piano STUDENTS at Curtis) with all the advantages (and disadvantages) that entails. I rather liked the close-knit, supportive atmosphere there, but you couldn't get a drink of water without someone knowing about it.
Juilliard is more diversified, owing to the fact that you have graduate programs and the drama and dance departments there. There's a greater variety and encouragement to explore (at least I found) the piano repertoire. Curtis is a germanic based school which emphasizes Bach, Beethoven, Mozart, Brahms, Schubert, etc.
And then you have the cities: Philadelphia is a wonderful, old metropolis with a wonderful orchestra but still pales in comparison with the frequency of performances one can hear compared to New York (I love the fact you can just walk over to the MET and hear some amazing opera performance).
My five years at Curtis was a great priviledge that time has only illumined, I doubt I'll ever feel that affection towards Juilliard, ever.
koji