i suspect oxford will be slightly cheaper. in cambridge, the university owns most of the centre of the city, and green belt land locks in the rest, so housing is in high demand.
Oxford has a very similar situation. The slight difference is that Oxford is bigger and the east of the city was a working industrial town like many in the Midlands, which still has an operating car factory making BMW Minis on the same site they were making cars in the 1960s, or even long before. But over time gentrification gradually expands further into that eastern industrial area. 30 years ago we used to say that as you went further east - SE more accurately - you first went through the bit where there were only students, then through the bit where they beat students up, and finally arrived in a place where they didn't know what students are, but this didn't mean it was safe, because they beat everyone up. It's more peaceful these days and the students have penetrated further east.