Tangible differences:
- Different teaching styles
- Different atmosphere/$$ that's flowing around at Oxbridge for various things
- Arguably being taught by better/more famous staff (in theory) for possibly some of the subjects, particularly in pre-clinical, basic sciences years than say a smaller, less well-known institutions (i.e. compared to some of the newer medical schools)
- Not particular to Oxbridge per se, but certain places have different rules for intercalation/degrees (i.e. Nottingham has an additional degree integrated -> fewer points, UEA only does Masters intercalation AFAIK)
- Better connections for non-medical stuffs. Considering the wealth/social disparity at Oxbridge, you would be far more likely to meet more (future) bankers, politicians and aristocrats there than at say, at HYMS. Connections are what you make of them.
- Partner universities for electives. General rule of thumb: similarly ranked unis have partnerships with each other. Useful to note if you want to go to Harvard or something for your elective I suppose (disclaimer: no idea which ones are partnered, but that's usually the case)
- Placement locations - though this is pot-luck + not terribly relevant for undergrad, but among the more "rural" towns, Oxbridge has more specialised tertiary hospitals where you may see interesting things. That being said, King's is meant to be a great liver centre, but I couldn't care any less about the complex things here. It's pointless at undergraduate level.
Non-tangible, more debatable points:
- Better outcomes? Yes, but also no. Better pass rates, but even then, it's not a great difference per se. Furthermore, the way recruitment works at the moment is by looking at outcomes by university cohorts (for foundation & the distinction bits in further training). Hence even if a guy in the bottom 20 at Oxbridge is an absolute genius compared to the 1'st place student in King's, the guy at King's would get more points. That being said, if the UK ends up going like the US (and a lot of other countries with national exams), it'd definitely be interesting to see objectively which medical schools are better, at least for exams.
- Smarter docs? Meh. Even at the moment, the Medical Schools Council has its members use common questions in finals. So the paper sat at any institution across the UK has common questions.
- Academic prospects? Meh. Unless you go abroad, at which point, it may be of benefit perhaps.
tl;dr
Does it matter if you're gonna become a doctor? No, except for some very fine points
Does it matter if you're not gonna be a doctor? Probably to an extent. But that begs the question: why go to med school. Go get a PPE degree...
NOTE: used random med schools to serve as examples. Please do not read anything into it. Nor reply saying HYMS is great you @!#%/ or UEA is better than Manchester etc. I'm sure they're all great.