I can kinda speak from both sides; I'm learning at WAP (albeit BAFC! Why not have a look at them? They have some lovely PA28 Warriors and their prices are comparable to WAC) and working on reception at PFT.
PFT's instructors are all professionals and very safety-conscious, as have heard that some people criticise them for not sending students flying when the weather's a bit dodgy. Clearly, this isn't a bad thing! I don't know how many of them are career instructors and, though I'd guess at the majority, I can only really speak for BAFC in this department. Prices there are reasonable and, while their aircraft aren't as good looking, as it were, as BAFC or WAC's, they're safe and fly fine so it doesn't really matter!
BAFC and WAC operate out of a very different airfield, which is smaller but really no less busy (just doesn't have the bizjets coming in and out of course!). BAFC staff, as I can't really speak for WAC, are all a lovely lot and very focussed and professional, all of whom are career instructors and many of whom have very considerable experience. I can guarantee that you wouldn't go wrong with them. Their Warriors are very well maintained too.
Maybe it'd be an idea to have a Trial Lesson at WAC, PFT and BAFC? That'll save you money in the long run as you'll be somewhere that you fit in. I know people who don't like BAFC because it doesn't feel "clubby" enough but, personally, it'd be my first choice every time and I've no regrets about flying there.