Still in a great dilemma.. Help me please!!!

As far as I know they are both good universities so I don't think it's possible for anyone to comment without knowing something about your priorities and goals. Why don't you say something about yourself?

Well.. I'm not so sure about what i'm going to do after the LL.M.. Probably, if i get the chance and the money(!!) a phd.. As far as i am concerned, i would like to work in the uk after the completion of my studies. I know that both universities have a great reputation and this is the reason of my dilemma.. Glasgow is a wonderful city but southampton is near london.. Well, these for now.. I hope i helped you :)

I don't see that your goals are so specific that you HAVE to go with one or the other... So to be honest I am not sure you can go very far wrong in chosing between those two. I would just advise you to find out as much as you can about both LLMs, universities and cities, and to go with your gut feeling in the end.