What makes Edinburgh special in that regard? As far as I can gather the admissions standards and support levels aren't in the same league as Oxbridge. League table results are fairly high for most subjects, but not any more so than some other russell group members.
According to various world rankings, it's top 20-40 and 5th or 6th in Britain and Europe.
But it's quite strong for CS/AI, as they have the largest CS department in Europe, producing the largest amount of world-leading research (according to the latest government-organised Research Assessment Exercise).
For undergrads that means there is an unparalleled variety of courses you can take, both in depth and breadth. I remember I had a choice of about 25 courses in my 3rd year and over 50 in my final year. For most British universities, your choice is rather limited - usually between 8-12 courses each year. Another bonus is that you get to work with leading researchers on your final year project. E.g. some of my friends were supervised by Phil Wadler - the guy was one of the principal inventors of Haskell and, with Gilad Bracha and Martin Odersky, designed Java generics and the extensions of the Collections framework.
So, Edinburgh is quite special and CS/AI is a particular focus at the University, so it's a shame not enough people know it.
Edinburgh is definitely not quite Oxbridge level on those factors. But it certainly is higher than the 'Red brick universities'. There are 24 universities in the Russell Group, and none of the red brick universities fall in the top 5 as it is an outdated term. It could be argued that Edinburgh falls in the top 5, which are comparable to the Ivy League.
