Need help: Tannoy or B&W?

I would suggest you listen to both of those speakers, quite different for sure. 

Night and day differences there I'd personally choose Tannoy but I am of course not you. Take some time and listen if you can.

Very different sounding speakers. I am not sure how to cross-shop those...

Um, what??

I wouldn't buy either unless you had heard them.  I mean, I have a strong preference, but because they sound so dissimilar. I'd say if you can't hear either skip them and stick to things you can listen to.

The Stirling III LZ looks great on paper, but has had mixed reviews - and it's hard to tell if that's just sour grapes from the distribution drama Tannoy went though recently, or something inherent in that model, OR just a bad sample that got sent out. Its 10" pepperpot driver SHOULD be capable of sounding great. 

I'm a die-hard lifelong Tannoy fan and own some 7 pairs now, including 2 sets of Canterbury (SE and GR). So I'm clearly biased towards that - the dual concentric sounds more natural and like music to me than multiple drivers all spread around. 

It's been a while since I heard B&W but it was first an older 802 Nautilus model that sounded very unnatural to me. No way! And then a Signature Diamond floorstander which I actually quite liked a lot - but nothing so much as to sway me from Tannoy :)

If you're looking at used B&W, maybe consider used Canterbury. Great model. The SE version is darker and thicker, and needs to be paired with gear accordingly (and probably supertweeters). The GR is extremely well voiced out of the box (no supertweeter needed).