(Original post by 0404343m)
I think all of those currently apply to both. Google some alumni: Adam Smith, Lord Kelvin in one, David Hume and Charles Darwin in the other. The list is as long as your arm at both.
Rankings wise: currently, they're about one place apart (14th and 15th). Infact, Glasgow is top 20 in all (rankings are stupid things at the best of times, but since we're using it as a reason) and ahead of Edinburgh in two, Edinburgh isn't top 20 in all at the moment. Historically- i.e. 20 years out of a 550 year old institution- they've tended to be about the same place- Glasgow has always had a higher dropout rate (possibly due to a higher percentage of local students who don't pay fees and have less tying them to the degree) which costs points. Otherwise, zilch to pick.
Internationally, Edinburgh does well. There's a good reason for this too: Look at global rankings and the places that place highly. There's an article on this somewhere if I can dig it up, but essentially, universities in capital cities place highly because academics are asked to rate 'best universities in Finland', or something. Since they probably know nothing about Finland, they write 'Helsinki' and hope for the best. This is partly why KCL and Edinburgh do very well in international tables (with peer review) and less well in national ones. Ask any German about their education system, and they'll tell you having Humboldt Berlin and Freie Berlin at the top of global tables is a nonsense: Internally they're nowhere, certainly not top three. This happens in many countries. I think if you ask Scots rather than undergraduates or school pupils on TSR, you'll get a different answer.
Where you're correct though is public schools in England. The further you go from Glasgow, the more people are likely to believe that the place is a grim, crime ridden hole, as if all of one city is a castle and the royal mile and all of the other is a council estate in Easterhouse. That outdated kind of reputation take s a long time to change, and there are still parents that won't allow their kids to go to Manchester, Glasgow, Dundee or Belfast, thinking of the time they were students in the 1970s. Edinburgh, despite having more than its fair share of dodgy areas, has avoided that. Glasgow has some horrendous crime rates- but nowhere near the university in the affluent and prosperous West End of the city.
If you go to the Old College of Edinburgh and walk around that area, and then compare it with the Gilbert Scott of Glasgow and the area around that, I'd honestly defy anyone to tell me that the former is better in any way. The problem is, and this is where 'prestige' comes into it, is that a reputation of a city probably means lots of privately educated kids will immediately write off Glasgow, not bother visiting, and then fawn over how amazingly brilliant Edinburgh is. I'm not saying it isn't, but having taught and researched at both and know numerous people at both, I'd say there's nothing to pick between them in terms of facilities, academics, standards. Give Glasgow City another 20 years to wipe the grim image of the 60s and 70s away, and I think we'd be having a very different conversation. After all, for hundreds of years they have existed to be the mirror of each other in the west and east of the country, primarily focused on serving the two regions where two thirds of Scotland live.
Fundamentally, I think there are bigger things to worry about rather than whether one huge, complex, institution is better overall than another huge, complex institution. TSR is permanently obsessed with 'Leeds vs Manchester' debates, as if having one on the CV is going to stop you getting the job compared to the graduate of the other. Even with Oxford and Cambridge, that hasn't been how it's worked for years now.
Edit: Also, ST13 was a table based on the highest ranked universities from the previous year's league table, i.e. 1999. That was full of problems (since some universities with relatively bad records on admitting students from poorer backgrounds like Exeter were omitted. The Sutton Trust themselves said once that had they used another year's tables, there'd be different institutions there), so they decided to go on the 30 'most selective' instead, and updated it in 2011. The way rankings go, it'd always have been dangerous to base things on one year from over a decade ago.