These two law schools dominate the Scottish law scene- the evidence tends to show that by graduating from the same university as the partners of the firm you apply to is the biggest factor in gaining an offer of employment. There's certain Edinburgh firms which take almost exclusively Edinburgh grads, and there's Glasgow firms who do pretty much the same. In terms of partners at major Scottish firms, they're streets ahead of the rest. The comment about chambers is ill-advised and incorrect (oh, wait, its Superhans, he'll have a brother who works in law employment, he's got relatives everywhere else to help him back up arguments), and both will stand you in just as good stead when converting to English law as anywhere else (save perhaps the LLB in English Law from Dundee).
In terms of entry, Edinburgh has a bit of a bizarre policy, where they put lots of weight on things like ECs and personal statement. I'm good friends with a law student from Edinburgh who was given an unconditional with AABB but rejected from Glasgow, and I know a Glasgow student with AAAAB who was rejected from Edinburgh. One is a little more concerned with grades, the other the things which come with your application. Standards of course, from what I can ascertain, are virtually identical, and both have some of the top names (Adam Tompkins at Glasgow, etc) in the field. The LNAT was a test a collection of Law schools (including Oxbridge) went into, but a few, including Cambridge, are drifting away from it- whether it sticks around only time will tell, but I wouldn't use that as a great indicator of quality. The OP should decide where they want to work- West of Scotland would slightly favour Glasgow, Lothian for Edinburgh- and this is a pretty big proportion of firms. Virtually nothing else to pick between them.
In terms of cities, Glasgow's still not shaken off its poor stereotype, and there's no denying that there's pockets of the city, mostly well away from the university, that have very high crime rates (although lawyers might relish this). I'd say Edinburgh is visually stunning and drier without the deprived areas (although its got its share of dodgy places) to the same extent as Glasgow. The West End of Glasgow where the university is can be considered a fair match for most of the capital though. Edinburgh is a bit more expensive since Glasgow still isn't perceived to be as desireable a place to live- but in my opinion, the fact that the university has a proper campus community, and the city has more pubs, clubs, live music, transport links, shops and students than anywhere else outside of London, would sway me (and it did five years ago, after much thought) towards Glasgow. You'll not be any better or worse off career wise because of the name of the degree from either- no employer would be daft enough to look dimly on an Edin grad because they only ask for BBBB and no LNAT for minimum entry.