To restate one of my earlier posts: the main difference is the structure which is remarkably different, the Oxford system consists of 3 papers taken for Mods at the end of the second term and all of the other exams at the end of the third year; with Cambridge 4 exams are taken at the end of the first year and then 5 a year thereafter. With Oxford Administrative Law and Jurisprudence are compulsory- neither are compulsory at Cambridge; the Cambridge system also means you take two extra subjects than your Oxford counterparts- in effect you get 4 extra choices which your Oxford counterparts will not get which can be taken from a wide range of subjects. For Cambridge Roman Law is still compulsory in the first year, whereas Oxford gives you a choice between Roman Law and Introduction to Law. Although personally I would take Roman Law- the subject is fascinating and gives you a good overview about how different areas of law interact.
Cambridge supervisions for each subject run for three terms whereas Oxford tutorials in each subject tend to run for one term but be considerably more frequent during that term.
I am told that Oxford is more theoretical and Cambridge is more black letter- I am yet to conclude on this myself, since taking Cambridge as an example there are a considerable number of Oxford educated lecturers and vice versa; some have taught at both institutions. Although from what I have seen essay questions are more common on Oxford law papers than on Cambridge ones which tend to have more problem questions.
Given the choice I would take the Cambridge law Tripos for undergraduate studies- ultimately it gives you more choice in choosing your options, so you can take a wide range of subjects. I do however believe that the Oxford BCL has the edge for postgraduate studies, it is an excellent course (but considerably hard work), which unlike many other courses (including the Cambridge LLM) is taught by lectures, seminars and tutorials.