Glasgow is much larger, and was more industrialized, than Edinburgh and is usually portrayed as suffering from a post-industrial malaise. However, it's a great place and the University has an excellent reputation.

Edinburgh is ridiculously picturesque and historical but it does have a reputation for being, when compared to Glasgow, of not nearly such a welcoming place.

I read statistics that it was the most violent city in Europe. During my 2 years there I didn't really see that side of the city- if you know what neighborhoods to avoid (like most other big cities) you'll be OK. I loved Glasgow- it has a great night life, interesting museums, great parks, wonderful people but the worst weather I've ever seen ;). After living in Glasgow, Edinburgh (granted I only spent 2 days there) seemed like "Disneyland Scotland"- very touristy and seemed a bit fake.