Differences that emerge farther down the road, and university maths is very different...
Cambridge Maths is all maths. But is easier to bail from. If you struggle, the Tripos system allows formal points of exit (to management studies or History and Philosophy of Science, for example)
Oxford's safety net is papers which have no equivalent at Cambridge (Single honours maths students can do the History of Mathematics as a finals paper, or join the university's ambassador scheme and teach maths at local schools, submitting essays on the experience). Properly bailing out of the course and onto another, excepting Maths and Stats, is less straightforwardly done, and certainly once in Y2.