I've shot a lot of different 9mm pistols over the years while conducting training - have yet to see a student that wouldn't let you try their pistol out. So while I don't own either of the two models you're interested in, I definitely prefer the M&P, which comes in a number of different configurations. The CORE version mentioned earlier is worth a thought when it is all going to be range play anyways - and you're not likely to see a whole lot of other people at the range with them either. And with the Apex trigger kits a lot of guys drop into them, they seem to be about as close to a single action trigger as you can get.
But you might want to cast your net wider before making your final choice. I happen to feel that the BHP works the best for me for ALL uses. Nothing beats a BHP for natural pointability. I'm aware that some complain it's "not super accurate", but you will notice if you start shooting the accuracy games like PPC, neither of the two pistols you inquired about are seen very often in the 1500 matches - nor the SIGs, Glock's, etc. None of them make the cut. If want the best in accuracy in a centerfire 9mm pistol, you should be considering the target versions on the 1911 platform. For accuracy games like PPC and Bullseye, the 1911 platform is the overwhelming choice. Anything else is like trying to win the revolver 1500 with a Colt or Ruger. Some may prefer DA/SA; for me and others, it is a non-starter even though many DA/SAs will let you work your way around it. I will take the "crappy" 4.5 lb trigger on my BHPs (complete with the magazine disconnects still in place) over a varying trigger pull every single day of the week (although some BHP triggers truly are ugly). And still others feel the CZ's are actually a much improved version of the BHP and therefore a better choice. If you really do want the nicest, crispest trigger pull available on a 9mm pistol, then the choice is simple: 1911 again. But most won't put the trigger above everything else either.
And then there's how people individually feel about tupperware versus steel.
So what I'm getting at is take your time and really look over what's available before buying - shoot as many different 9mms as possible. Look at your targets instead of just banging away, so you can see not only which pistols feel best in your hands, but if you're grouping with one is a bit better than the rest of the herd. It's not like trying a bunch of different pistols, shooting them, etc is drudgery and a painful chore! I love the chance to try out a firearm that I've never had in my hands before.
I'd also make sure of my purchase criteria. How much is "dare to be different" worth? If I shot best with a Glock, I wouldn't care if everybody else I knew owned one - I'd buy a Glock. For me, it is mostly about comfort/ease in use and how well I can shoot with it - most of the other considerations are a distant second. I would be looking at how easy it would be to make changes in the fit (by comparison, about all you can do with a BHP if it doesn't feel right is change the grips), aftermarket trigger kits, conversion kits, changing the sights, etc. It would suck to be stuck with a pistol you didn't care for if the glitter of being different ever wore out.
The goal is to pick the pistol that your hands, eyes, and brain says is best for YOU - not the pistol that me or anyone else says you should be picking or looking at. Really no different than picking a rifle, shotgun, bird dog breed, etc. Take your time and have a lot of fine with the different candidates before making your choice. Think of it as the dating before the marriage...
Those are my suggestions and I'm sticking to them.