Public schools are what I'm talking about - the ones people would actually transfer to. (UCB, UCLA, UW (where I went), UT Austin - all top ranked CS program schools) Private is much worse. You'll probably never get into a top private school unless you're transferring from another top tier institution - most people I saw transferring into such schools were already from other top tier schools. Stanford, for instance, accepted 27 transfer students last year. 27 - that's it. Same story for many other prestigious colleges.
The point of going to a top program isn't that it's a better program academically (maybe it is - maybe it isn't). It's about the resume and other things the university offers. Some of the schools help place you in co-op programs, have catered career fairs, and much more. They can set you far apart from other "lower tier" schools and make you stand out in the overwhelming crowd of new grads. It's mostly about signalling more than anything.