@AceofallTrades, I know a number of current and recent students at both places, and they are both great schools. The exchange rate right this minute is quite favorable, but of course that can change, and there is no telling what it will be like in a year or two or three.
You may know pretty quickly if one of them is a poor fit for you, but it may not be as easy to tell which is the better fit- mostly b/c most people change a lot during the first year of uni. So, StAs may feel cosy/safe/easy this year- and in two years it may feel the same way, or feel small, claustrophobic and isolated. Edinburgh may feel big/urban/hard this year - and in two years may the same way, or feel comfortable and easy. In both places try and push past the excitement/challenge of the new and imagine daily life. Swishy red robes are great- but it’s only a tiny part of the overall experience, so don’t fall in love with the glamour of it!
Some random similarities & differences:
There are Americans at both places, but they are a bigger proportion of the student body at StAs (~20+%/forgetting the exact # this year), and as importantly, they work hard to make it easy/easier of the US students. Edinburgh will not hand-hold as much.
Most students live out (ie, not in university housing) after the first year at both places, so look at the kinds of places you may be living after first year. You are more likely to be sure of getting on-campus housing after first year (if you want it) at Edinburgh than StAs.
Both places have really, really short days in the winter (basically, it is dark from 3:30ish in the afternoon until 8:30/9ish in the morning). Try walking between areas that you are likely to spend time in (classrooms/on and off campus student housing, for example).
Student societies are an important part of social life in both places. Take a look at the notice boards for what’s going on. Both will have a ‘freshers week’, where all the societies pitch their wares. If you have some particular interests, look at those spaces/activities.
Finally, look closely at the course list for each year of the program at both places- that will matter more than you might realize.
Good luck- and remember that you are deciding between two good choices- there isn’t a ‘wrong’ choice!