Both of mine print exactly the same with the variety of ammo I commonly carry and use. By that I mean the POI is directly under the front dot's NS capsule out to 15yds, in my hands, like the old Ashley Express and now the XS company shows in their literature. (Moves to top of 'dot' at longer distances.)
I've tried a variety lot of different loads for accuracy, and also checking for bullet pull. The ones I found printed nicely, tightly and to POA in my M&P 340's, in my hands ...
.38 SPL:
The old 158gr +P LHP (Rem & W-W).
Speer 135gr +P GDHP
W-W 130gr +P RA38B (same as PDX1 commercially packaged).
Rem 125gr +P GS, but they became harder to find locally, and when I went to replace them found it annoying that the company had decided to go from 25rd boxes to 20rd boxes. Having the extra 5rds used to be an advertising and selling point for Remington when the 20rd box craze came along for everyone else.
Speer 125gr +P GS (I mostly save it for range fodder, since that older 125gr GD wasn't really designed for barrels shorter than 4").
Hornady 110gr standard pressure CD(FTX). I really only got that standard pressure load for us in my 37DAO, since it was made on the older Airweight frame, but I ran some through my M&P's, and it showed itself to be a tack-driver (again, in my M&P's, in my hands).
.357MAG:
Rem 125gr SJHP
W-W 145gr STHP
Fed 130gr Hydra-Shok
I tried some other Magnum loads, but they either exhibited signs of bullet pull, and/or the heavier bullet weights offered more recoil 'slam' against my palm than I desired to be able to run fast and controllable shot-strings.
I got my first M&P 340 when they were first announced. At that time I was still able to call the company and get an armorer discount to directly order a gun (and have it shipped to my cop shop FFL for the paperwork). The LE sales person told me I was getting one from the first production run of the new model. Aside, from the artfully covered up screwdriver gouge around the yoke screw (covered with apparently black marker, which came off the first time I cleaned it), it was a very nice example. I'd bought it as a ranger beater and off-duty weapon, so the cosmetic scar was only annoying. It's acquired a lot more dings, dents, scratches and signs of wear since then.
I bought the second one when they decided to offer a model without the ILS (aka No-Lock model). Why not? It seemed a good excuse to buy another one. (And I could still get the LE discount.)
They've both taking a bit of a pounding, as I bought them as shooters (and had access to a LE range inventory that stocked .38SPL and +P), and I burned up some Magnum loads just to keep things interesting. (And to prove I could.)
I haven't really kept up with the S&W catalog for a while, but it looks like the version with the Lock, and the M&P 360, aren't in the current catalog. Just the M&P 340 No-Lock version.
FWIW, I didn't order mine because they were chambered in .357MAG. I was primarily interested in the XS NS set up, the Scandium-alloyed aluminum frame and the blackened (PVD) stainless cylinder. I'd have ordered the gun if it had only been chambered in .38SPL +P. If I remember right, many years ago LAPD ordered a version chambered in .38SPL +P, available for sale to its officers through its academy store, but I can't remember if it had the ILS (Lock) or not.
I added some UM boot grips to both of mine, which added an ounce to the weight.