I'm going to disagree with Elsie above - I think whether you go to Edinburgh or Aberdeen will have minimal impact on a future ability to pursue a legal career.
They are both strong universities, I went to York which is ranked around the same place as Aberdeen in league tables and that wasn't a barrier to me or any of my friends and peers pursuing successful legal careers in the regions, or London, or even the bar - although the bar is a bit of a special case and all of my friends who made it to the bar stand out as particularly gifted in their own way.
From the solicitor perspective, and OK all hiring managers are different, I review c30+ CVs a year for junior solicitor recruitment into my team (I work inhouse at a large UK corporate), if I saw Aberdeen or Edinburgh I would simply note "good university", check the classification, and then move on to the rest of the CV.
Re choosing between the two, consider course content, uni societies and wider groups to get involved in, and of course fit - where you would feel more comfortable - I enjoyed studying at a smaller campus uni and wouldn't have enjoyed bigger city life as a student - we're all different. Edinburgh *could* make it easier to obtain legal work experience simply by you being geographically nearer more of it - that's the sole advantage in my view, but if you're happy to travel for the all important vac schemes and work exp if you source it outside of Aberdeen, no problem.
In short - Look at the wider picture, what will you enjoy, and where would you feel happy studying and living. If the answer is Aberdeen then go for it it, and don't worry about minute differences in university rankings - it doesn't matter.