There are similarities, but there are also substantial differences between the two courses, particularly in structure. At Cambridge you take 4 courses, which tend to follow a 2 hour lecture/seminar a week structure throughout the year (there are generally no supervisions on the LL.M.). The B.C.L.’s structure depends upon which courses you take, but it can vary. Most subjects have 2 hour seminars (some have lectures in addition to this) each week, or every other week, but in addition to these you also have tutorials- some subjects have 3 or 4 of these, others 8. These are not necessarily throughout the year- some courses are relatively intensive, others more spread out. If you are looking for small group interaction the B.C.L. probably would be a better choice.
In the LL.M everyone (common lawyers or not) takes the same examination, and answers the same number of questions (generally 3). At Oxford non-common lawyers are distinguished, taking the M.Jur which means whilst they take the same exam they write 3 questions, and the B.C.Ls 4, (there are however some exceptions to this). Some of the papers on the LL.M are open book, with the B.C.L they are closed book.
In addition to this each University has its legal specialisms. Oxford has a traditional reputation for private law, Cambridge for public international law, but this does not mean that good scholars in both disciplines aren’t to be found at both. There are however some subjects where one University has an edge over the other though. Take Jurisprudence for instance, Oxford has a higher concentration of such specialists, and has a formidable reputation in this field. Legal History- this is one of Cambridge’s more renowned fields with Baker, Ibbetson, and Milsom (although Milsom holds an emeritus position). International Law, Oxford has some good scholars, but with the concentration at Cambridge and the Lauterpacht Centre this would be in favour of Cambridge. Conflicts, Cambridge’s Fentiman and Rogerson are good, but Briggs at Oxford really needs to be experienced, preferably in a small group setting.
From what I have seen the Bar seems to hold the B.C.L in slightly higher esteem. I hope this is impartial!