There is a gulf in undergraduate teaching between Oxbridge and the pack. The supervision system guarantees all Oxbridge students weekly, small-group tutorials, organised and paid for by the colleges, which retain much more academic involvement than other collegiate universities like Durham and York (whose colleges are mainly residences with pastoral care and sports teams). If you go to Oxbridge as an undergrad, you'll be pushed hard and closely supported.
The second gulf is of course the selection effect of every bright child in the UK having Oxford or Cambridge as their first university pick. No-one from an older generation would advise any teenager to do otherwise. (Incidentally, I'm acutely aware that Durham first, then Cambridge is lower social status than vice versa. Because I didn't get in at 17). Everyone knows about this, and we could debate how reputations change, but I suspect my point above about the supervisions system for undergraduate teaching is less well-known.
I could also mention the gulf in wealth between universities (which pays for those supervisions, book grants etc), in age (Oxbridge actively lobbied against new universities in England for hundreds of years), which has a consequence for historic buildings, famous names and prizes, and so on. It all creates an almost unbreakable flywheel of reputational lead for Oxbridge that would take generations to overturn.