To be honest, it doesn't really matter that much - the course is similar everywhere, with possible differences in whether there's an optional module (I think ULaw will oblige you to do company law; City will do a whole module in EU law; and Birkbeck will give you a couple of optional modules including mooting.
City is probably the leading option for aspiring barristers, but far more important than institution are (a) your results in the GDL and (b) your results (and sometimes the institution) of your first degree, so don't feel bound by this consensus. Plenty of people get pupillage after a BPP GDL (and doubtless also Birkbeck, although that's a much smaller pool so I don't know for sure).