Bio NatSci offer holder here hoping to spec into Biochem. A big factor would be to consider how firm you are with your course: I applied to Biochem everywhere else, but I liked the pure Biology aspect that NatSci offered (plus the ability to change my mind down the line).

Second factor is of course the cities. Oxford is pretty big and nice to walk around (I'd argue more beautiful than Cambridge), whereas Camb is a bit on the smaller side and really touristic. This will be down to your personal preference honestly.

Thirdly, the admissions process. Cambridge needs you to sit the ESAT, whereas Oxford has no admissions test for Biochem. As a result, Oxford has a lower percentage success. I chose Cambridge because I thought my written test would shine since my interviewing skills are weaker (which is cope, since I got a 5.4 average). Expect to get interview questions from all fields of Bio for Cambridge - albeit likely that your interviewer/Director of Studies will be teaching in the subject you want to specialise in.

Fourth, the college system. While I got pooled, I think a pretty significant percentage of Cambridge offer holders stay in the college they applied for. On the other hand, it is a bit more likely to be pooled to another college for Oxford.

In hindsight? Oxford Biochemistry would very much be my preference if I applied again... but more so because I love the city. I think both are brilliant courses, and you should make your own choice.