I am at City for my BVC having done my GDL at BPP.
City is, in most ways, smaller. This is good (feels more individual) and bad (much shorter library hours). At the same time, at City you have access to all the resources of a real university, if those appeal to you (e.g. student union bar, wider range of clubs and societies, more external talks on a range of subjects including non-law, etc.)
The admin staff at City are about 10,000 times more competent than the ones I dealt with at BPP. The teaching at BPP was good, but the admin stank.
I doubt there is much difference between the different providers in terms of the actual course. The BSB regulates the BVC to within an inch of its life (what books have to be in the library, the maximum number of students per group, the types of assessments). And no one I’ve talked to will admit that chambers care where you get your BVC, only that you have one.
In a general sense, I’d be wary of Kaplan since it’s their first year offering this course and there are bound to be teething problems, but that’s a general observation, no slight on Kaplan in particular.