Some med schools don't like applicants doing further maths (they don't count further maths as one of your three A-levels). Since further maths would be your fourth A-level and fifth AS, you would still be able to apply to them, but I think they would probably find the EPQ more impressive.
In previous years, one advantage of further maths for Cambridge specifically is that it is easier to guarantee high UMS in maths and further maths modules than in other subjects. So if you were very good at maths, you could get 100% UMS in further maths giving you a higher average (and a possible advantage) over someone whose fourth subject was history. I don't think this applies any more for most applicants, as AS's are being scrapped, so Cambridge won't ask for your UMS.
Also, it's worth noting that Oxbridge has very little advantage over other universities for medicine, unless you want to go into research. If you are in the lucky position of having good enough grades to be in with a good shot at all med schools, you should apply based on their specialisms in medicine and teaching styles, rather than perceived prestige or teaching quality.