It depends what exactly you're comparing. I've studied at both Cambridge and Nottingham and they're simply very different.
Prestige in many senses is going to be very difficult to beat but also very subjective. Everything about Oxford and Cambridge screams of tradition and heritage. You only need to walk round the grounds and colleges, look at some of the activities, and listen to a lot of the terminology and traditions that still exist.
I would say that reputation is different though. There are lots of universities that hold strong reputations both in and out of the country. There's no point listing them, because there's dozens that when a lot of people hear the name, they go, "Ah, that's a good university."
Then there's specialist areas. Loughborough is the best at competitive sport, there are only 8 universities which teach veterinary sciences, and then some people like the type/time of builds e.g. redbrick institutions.
In terms of research quality and output, we'll see later next year when REF outcomes are published, but lots of international league tables make a good attempt at measuring the research reputation of institutions as well as their individual schools/departments/faculties. There are lots of instances where UK universities are ranked higher than Oxbridge in both domestic and international league tables, which are perhaps given more time of day than is needed.
Of course, if you take student satisfaction, NSS results show the Open University is the best by far.
If you want to compare students' unions, Oxbridge do things so much in colleges that their SUs are totally different to other universities', and as such students rate them lower down. Sheffield and Leeds came out on top last year.
Universities are so diverse and unique that it's very difficult to come up with an overall reputation/prestige measure imo.