Medicine at Oxford and Cambridge is quite similar in that, unlike a lot of other medical schools in the UK, they've both retained a two-stage medical course where the first three years are pre-clinical years where you learn about the scientific basis of medicine, earning a BA in Clinical Sciences (or something like that) and then the next three years are clinical years with patient contact. The main points to note, I think, are:
1. Cambridge lets you do anything you like in the third year regardless of whether it's related to medicine. Oxford, on the other hand, often makes its students do a research project in the third year.
2. They both have competitive entry to the clinical stage so that not everybody who gets into medicine at either of these institutions is guaranteed to stay for the full six years. Rhetorical Hips, who starts medicine at Cambridge this year, has said elsewhere that this policy is being reconsidered by Cambridge and possibly by Oxford so bear that in mind. Generally if an Oxbridge student doesn't make it to the clinical stage at their university, they tend to go for universities in London, which often have special arrangements for Oxbridge students in this situation (Imperial, at least, makes special reference to them on its website).
Beyond that, it's your preference. Generally speaking it's better to apply to your strengths. Unless you've got straight A*s at both GCSE and A-level with impressive extracurriculars, the choice will usually be obvious (e.g. if you have strong GCSE results but your AS UMS isn't that great, then Oxford is the obvious choice; if the other way around, then Cambridge).