Studying in Britain takes you places intellectually that an American university experience simply cannot, emphasizing rigor, self-reliance, and a scholarly sense of irony. As much as one may hear about quaint traditions and see examples of remarkable historical continuity on a daily basis, it is this serious intellectual tradition that counts most. A strong grounding in your subject and an expansive curiosity are simply expected, and you learn to respond to this expectation. Feedback from supervisors is generally neither too little nor too much; fellow students, in my faculty certainly, are future professionals; and the opportunities to train your mind are everywhere.
Social life at Cambridge revolves around the college- and makes it obvious how much happier are graduate students in the UK than their US counterparts. As a result, people are open and friendly, ready for everything from ceilidhs (Scottish dancing) to long, langurous nights at the pub (naturally).