Hey! I was successful for e&m this year, and people are right - the offer rate is ridiculously low. However, I'd say whichever you have a better chance in getting in for is going to be _very_ personal.
Cambridge's entrance exams in economics require very strong maths skills, where oxfords simply don't. that means if youre not a maths genius, your cambridge entrance exam score will be comparatively low compared to others. The oxford entrance exam is 50 multiple choice questions, 25 problem solving, 25 critical thinking. unfortunately, i think this exam is very much an either you can do it or you cant kind of thing, and improvement over time is fairly difficult since it comes across as an IQ test if im being entirely honest.
Another note on entrance exams - oxford scrapped the essay half for e&m this year, cambridge still have an essay section
I'd do a practice paper in both, and see which you get on with better
secondly, cambridge will basically guarantee you an interview, and ox interviews only 3 people per place. This means that if you _know_ you are good at talking through your thoughts process, but find the entrance exams harder, then its easier to get an interview for cambridge and prove yourself there. However, i thought my interview would be the weakest part of my application, and it ended up being the strongest, so its very difficult to judge this one hahah
since most applicants at Cambridge are invited for interview, the process is fairly holistic - when considering your application, they are likely to take into account all parts of your application equally. Oxfords is a little different - you need to have good grades and perform well at the entrance exams to get an interview, but there is a ridiculously close correlation between interview score and offers. This means the entrance exam "gets your foot in the door" but once youve got to the interview stage, that may as well be all that matters.
I also wanted to mention after the offers: cambridge's standard offer is A*A*A, BUT when you look at the offers by college, a fair few require an A* in further maths... I was predicted an A* right up until January, but partially because of lockdown and partially because further maths is far rougher than anyone expects (second year really is much harder than first year, trust me) I'm looking at a B. Cambridge have no flexibility when it comes to hitting the offer as well, as when you dont hit the offer, theyll replace you with someone from the summer pool that did. I would really heavily discourage anyone from allowing their oxbridge fate to rest on a further maths grade, since thats a recipe for disaster and extreme stress
Oxfords offer is A*AA including maths, which is ridiculously reasonable, especially if you do 4 subjects.
Finally, since cambridge has such tough entry requirements, theres some self selection where many (esp those that didnt take further maths) apply to oxford instead, so theres some self selection going on there which means that offer rate absolutely is not the be all and end all, or even that reflective of how difficult it is to get in
So yeah, since the application processes are so different, it depends fully on your strengths.
Hope this helps!