I’m studying Computer Science and Philosophy right now, and there were a couple of factors which made a difference. The first was my passion for the humanities, and the fact that Oxford tutorials in essay-based subjects are often significantly better than tutorials for science subjects (where you simply go over a problem sheet). Oxford is definitely one of the top hubs for philosophy in the world, and there are hundreds of students studying it, so you’re in good company. I’m also very strongly inclined towards analytic philosophy, which is Oxford’s specialty.

The second is the specific curriculum breakdown for Computer Science and Philosophy vs Computer Science. In the former course, you end up skipping classes like Linear Algebra, Continuous Mathematics and some of the more low-level CS classes, in order to have time for philosophy essays. Since I had already done a lot of mathematics, and am more interested in theoretical computer science, I was pretty happy with that tradeoff. More engineering-minded people may well feel differently. Overall, I’d encourage you to look at the specifics of what classes you’d get to take in both options, and have a look at some of the lecture topics, before deciding.