What are the European equivalents of famous American music schools such as Juilliard and Curtis?

I agree with the previous answer's suggestions, but I'd add two in France, who is conspicuously absent from the above list; the Conservatoire de Paris and the Conservatoire de Lyon. Surprisingly, the latter is more prestigious than the former. I'm not sure if this qualifies for your list, but an institution of equal or greater prestige to any in France is the American Conservatory in Fontainbleau (where Nadia Boulanger taught most of her supposed 600+ students).