I don't actually know tbh but
this thread may be of use to you. If you mean competition in the sense of the amount of people you're competing against, you'll be competing against less people for sure...but remember, the people you will be competing against will most likely be impeccable candidates (usually need a high 2:1/ 1st for postgrad courses, strong references, etc). That was just a comment about postgrad courses in general though, I'm not sure if the postgrad courses at Oxford are easier to get into than the undergrad course. I think that for maths, everyone who gets a 1st in 3rd year at Cambridge gets access to Part III (4th year) so it may be easier than the sense that it removes the nerve-wracking interview part which you have to go through when applying as an A level student but tbh, I'd think getting a 1st on the Mathematical Tripos would a lot harder.
Edit: don't even know why I'm talking about maths.
Just an example of a specific course I know so bleh.