Edinburgh is possibly the most beautiful city in the world. Glasgow is more rough around the edges, though ignoring one or two areas you won't be in it doesn't live up to it's reputation.
The population of Edinburgh is 500k, Glasgow is 600k with a bigger population in surrounding areas so it feels like a significantly bigger city. After 5 years in Edinburgh I felt like I couldn't walk around the city centre without bumping into someone I know. I think people who live in the Edinburgh suburbs and nearby towns are less inclined to go into the city centre than those in Glasgow so when you minus tourists central Edinburgh feels quieter than other city's it's size do. I think a lot of it is to do with the Glasgow area having a better train system into the city centre. Not that transport in Edinburgh is bad, the buses will get you everywhere you cant walk.
Both are proper sized cities so have everything you'd expect of a city, there's just a bit more of everything in Glasgow. Like both have a music scene and venues but Glasgow's has that bit more to it. They are only 50mins on the train apart.
Both are reasonable big unis plenty going on in terms of unions/societies. Glasgow has two unions which are a bit competitive, you join one and you stick with it. On one hand the competition is good and brings variety but on the other hand it means you don't have access to everything. Edinburgh just has one union (though it has several buildings).
Edinburgh uni feels much more part of the city centre. The uni is in the middle of the old town (Old Town and New are the too halves of the city centre) and all students tend to live on the edges of the Old Town. Glasgow uni is in the west end but a few stops on the underground from the city centre. The West end feels a bit like a student suburb, a but more bohemian.
I'm not sure what else to say off the top of my head but I'd be happy to answer any more specific questions- I lived in Edinburgh but I'm from in between the two and have spent a fair bit of time in Glasgow. Based on what you did say I think your main consideration is city size. Glasgow feels more big city, Edinburgh feels like a small city. If you want as much stuff to do as possible then go Glasgow. If you want stuff to do without feeling like you're in a big city then go Edinburgh.