This begs the question as to what constitutes being more conservative and whether this is a good thing.
I think that many might see Oxford as more conservative but the reasons for this are sometimes a bit nebulous. Oxford is the older university (although only slightly, relative to their overall ages) and several things at Cambridge are older than their more famous equivalents at Oxford. The Cambridge Union is older than the Oxford Union. The Cambridge Printing Press is older than Oxford's.
Maybe it's because of Cambridge's long reputation in the sciences, dependent on new discovery, that it has less of a conservative image with some than Oxford.
But if 'conservative' is associated with respecting tradition then the continued tradition of the wearing of gowns for exams at Oxford may make it appear more conservative, if only in a very infrequent ceremonial way.
It wasn't especially conservative of Oxford to refuse to give one of its graduates Margaret Thatcher an honourary doctorate.
But I think that Oxford is more conservative because Cambridge has made some of the most notable advances (e.g. in Philosophy and Economics) in what was traditionally supposed to be Oxford's main territory, the arts.