I own a BP currently and I feel like I could give you some of my thoughts I gathered from the posted V3 pics...
The bezel:
The font is too thin, yet quite correct. I could see no difference in the fonts between V3 and BP. The BP often has the numbers off centered. QC issue...
The angle of the ceramic insert is clearly wrong. The V3 bezel seems correct.
Crystal height is wrong on both of them, but the BP is worse.
The clicking action on the BP felt kinda seized and it was difficult to turn - you'll read that often. I disassembled the bezel, replaced the double sided tape and cut it right, lightly greased it and reassembled it. The clicking feel is now amazing!
Let's say The BP bezel is a typical lack of QC. I heard the V2 bezel feels amazingly out of the box, but I can't comment on this. btw: The BP bezel has very little play if you wiggle it cw - ccw. This is due to the ratchet pin being 0.2 mm smaller than the hole it fits in.
The bezel itself is much too low profiled on the BP. You'll also feel it when turning it. Your hand tend to slip over it (after owning a noob v1 which is known to have a very loose bezel I kind of like it though

) However the V3 looks amazingly good in this point.
The bracelet:
No question - the V3 wins in terms of looks and probably esthetics.
The SELs are already good on the BP, but stick out too far and have that sharp edge on the bottom the gen doesn't.
The V3 SELs look convincing to me and I have faith in them to be the first ever correct Rolex SELs on any rep

The threads on the BP suck arse. The screws also look cheap. MUCH MUCH better on the noobs V2 and V3. I'd say the V2 and V3 screws and links look gen.
The clap on the BP is not even worth mentioning it. It doesn't lock, it feels and looks cheap and the safety buckle won't even close on mine. From what I've heard the V2 clasp was amazing. I doubt the V3 clasp is much worse, however I saw they messed a bit with the gaps on the V3 clasp.
Dials:
Except for the lume application the BP dial is perfect imho. I love it! The lume (although it does it job very well in terms of glowing

) is applied very unevenly and I could spot impurities etc.
I never liked the noob dials. I know the fat hour markers aren't really a flaw, because there was a series of gens who had these hour markers as well, but I don't like their looks... You can judge yourself.
Btw: Why is everyone saying the Rolex crown is such a flaw on the V3???
Hands:
I like the BP and the V3 hands, but again, my BP hands look as dirty as if someone found them on the highway...
My BP was very dusty on the inside anyways :culpability:
The crystal:
I like both crystals. they both feature very good LEC and have AR'd cyclops. Side note: my BP cyclops was twisted which is annoying, again a QC issue...
The case:
The case on my BP is amazingly good. The finish is a bit too shiny, but nothing one couldn't fix.
The crown guards on the BP are spot on as well as the lugs and everything else. That was a big flaw on the V2, but they seemingly fixed the CG on the V3.
I think the V3 case went very well.
The crown:
The crown position on both of the BP and the V3 is too low compared to the gen, but honestly - who cares?
The quality of the BP crown is SHIT! Swap it! My noob V1 crown felt pretty ok, so I presume the V3 crown will be good as well.
Last but not least, the pearl:
I was amazed how the BP pearl looked when it was released, but looking closely the noob wins again. It has a better shape (the BP is just cylindrical) and the lume on my BP isn't applied very well. QC issue again -.-
All in all the V3 wins in my eyes. I would try to get a V3 and swap the dial, or at least the hour markers. If you have too much cash left over look for a gen bezel and you're done!
Cheers