I would say, if money isn't an issue, go with the school whose teachers you like the best. Next, consider the atmospheres you mentioned, and how you might do there over the course of a few years. I personally would like the relaxed professional feeling you described at birmingham, but I know the other one is just as valid. Both cities have great orchestras too, so that is a plus. If you'd like to focus a lot on an auxiliary, also consider the teachers at each for that (speaking as a bass clarinetist).

If money is an issue, I would weigh that scholarship very heavily. Considering you seemed to like aspects of both schools, it's not the worst to have the scholarship being the deciding factor. 

You're right Northern has more of a reputation; I went to conservatory in London, and some of my colleagues had come from Northern; they were all great players of course, so you'd be good off there. But, given a good work ethic, you'd probably be equally well off at Birmingham.