In reality, they're very close academically, and I don't think there's really any way to gauge whether one is better than the other.
I would also take into consideration each school's location, as you'll find one may suit you over the other, and you'll be spending a year of your life there. Bath is smaller but has tons of history and Roman architecture, and Birmingham is bigger and perhaps livelier, depending on who you talk to, of course.
In reality, they're very close academically, and I don't think there's really any way to gauge whether one is better than the other.
I would also take into consideration each school's location, as you'll find one may suit you over the other, and you'll be spending a year of your life there. Bath is smaller but has tons of history and Roman architecture, and Birmingham is bigger and perhaps livelier, depending on who you talk to, of course.