Rather more Oxford people show up on these threads. Mine was in the last year at Cambridge to be permitted to go to London for their clinical years. They did that for a number of reasons including what they thought would be easier travel to placements. It's certainly worth looking hard at where they might be sent on placement and also at where they live in both pre clinical and clinical years. The preclinical Cambridge/ clinical London was a popular choice and I agree it's a bit of a pity it isnt an option now.
After 6 years in one place some students are keen to move on but others may have taken root. Quite a lot of medical students choose to apply for F1 in the same deanery they studied in. Settling in to F1 when you already know the hospitals and staff may be slightly easier. Of course Oxbridge students do often try to head for London at F1 and that's an extremely competitive application process. If they want to make it to the most competitive deaneries they need to start thinking early on about how the points system works. Cambridge students wanting to stay in the area dont have much problem as it's not a competitive deanery.
Oxbridge students tend to be good at passing exams and they go on to be good at passing specialty exams. Mine does think that the nature of the Cambridge course probably helps with specialty exams. But plenty of students at other medical school are also good at passing exams.
Cambridge tends to turn out more surgeons, no idea why although I think it's still doing dissection not prosection and maybe that attracts those who want to be surgeons.. It also seems to be easier for medics to be friends with non-medics, although now they all stay in one place obviously the bonds with other medics will tend to be stronger.
Cambridge is the bigger medical school and interviews more people than Oxford (in non-covid years). At least some of the colleges place more emphasis on academic record than interview. So you'll be interviewed if your entrance exam and academics show you can manage the course and then need to demonstrate that the teaching style will suit you. Cambridge had ( I havent checked recently) the higher grade requirement for its course so less applicants per place but all academically very able. Oxford places more emphasis on being the right type for Oxford.
Once you are an F1 its not going to matter much which medical school you went to, it will matter how you have done in your training.
Imperial and UCL actually do very little more clinical stuff in the first 3 years than Oxbridge.
Visit both places, talk to a lot of medical students. Oxford is said to have better clubs, if clubbing appeals. Cambridge gets pretty cold in winter.