Down South, the outdated reputation of the city of Glasgow probably hurts the University's reputation, and the size of St Andrews/ a certain event in 1999 seem to make it seem elite. In terms of actual academic standards, theres nothing to pick between Glasgow/Edinburgh/St Andrews, and most in the central belt of Scotland (and indeed the UK) would see those three as the best. In Scotland, they'd probably be considered equal, and probably in much of England, while most would regard the academic standards as pretty nigh on identical (they are, just no one seems to understand stats these days), Glasgow would probably be edged out based on ye olde view the city is a dump. This will (probably) change with the generations though- most teachers and parents remember Glasgow of the 70s, which in turn trickles through to teenagers. Thousands aren't put off though, out of around 30,000 applicants per year, 10,000 are from outwith Scotland. They're all the best known abroad too- well at least from people I know in and out of academia in North America- they're usually the only three they've heard of. Usually its because of the cities, St Andrews has the royal connection thats put it on the American's radar, and caused thousands of eligible young girls from the States to apply in 1999. Funny that. In terms of the money they turnover and draw in from their research, Glasgow and Edinburgh together outperform the rest of the Scottish Universities put together- research wise, they're certainly on the radar among the largest ten in the UK. St Andrews obviously is hindered by its location, so produces comparitively very little, but what it does do is usually high quality.
Aberdeen is probably next, and its ability to attract the very best on a consistent basis (although there are many good students there) in terms of both applicants and staff, is hampered by its location, as Andrew Marr would say "on the periphery of the British experience, remote from the central belt of Scotland nevermind London" (he was actually talking of oil industry here, but meh, same difference). Again, its location hits it rep, although unlike Glasgow its not thought of as rough, merely cold, wet and remote. St Andrews by comparison is a full two hours closer to most of the major English cities, and around one hour from Edinburgh. Reputation among the public and reputation among people in the know are two totally different things though.
After this, Strathclyde/ Heriot Watt or Dundee, followed by Stirling- aka the 60s Unis. All broadly similar, Dundee's link with St Andrews and Strathclyde's resources by being in the middle of most of Scotland's population have meant in general they've been able to compete in lots of areas with the ancients. After this, it doesn't really matter. Not that RGU or Caledonian aren't good for certain things (notably pharmacy or optometry), merely that to compare an institution which really only has two or three areas and dozens of weaker ones, is probably unfair to the institution in question. I certainly wouldn't look down on anymore for attending Caledonian for certain subjects, or Abertay for its Computer Games course, thanks to its links with Rockstar, its probably one of the best places to go.