The most accurate full size M&P I have is a newly built up 2.0 .40 slide on an older 2.0 9MM frame.
Got the barrel from KKM Precision. Awesome fit. Nice groups. Likes the Winchester 180 grain hollow points.
KKM Precision - https://kkmprecision.com/product-category/mp/ This link is for the 5" .40 but they also do the 4&1/4". Thread or non-threaded.
Just because -
Attached FileA word about that barrel. I was told, after installing a file to fit barrel in the FDE 5" 9MM that didn't require any metal removal from the bottom of the barrel lug that my factory frame locking lug must be out of spec. I never replaced it. When I got the KKM barrel I tried it in my 2.0 .40 4&1/4" Performance Shop pistol and it wouldn't begin to move all the way to the rear due to contact between the locking lug in that Performance Center pistol's locking lug and the barrel lug. However, it slid right onto the 2.0 9MM frame with only a small "bump" from contact with the locking lug. So I put it on the 9MM frame and it worked great.
I'm not saying the KKM barrel was "bad". I'm saying it was what it's advertised as. A barrel that requires some fitting. It just happened that the area it was oversized in was perfect for an M&P locking lug that was too short in height from the start. Based on recommendations from others on the M&P pistol form and a good friend I bought that barrel and based on it's performance I'll buy another one when I need it for a different project/build.
I have two 2.0 M&P .40's. That 5" FDE gun and a factory 4&1/4" PC gun. The PC gun does not match that made up .40 for group size and even though I thought I could live with the PC trigger I find myself noticing the difference every time I have both guns at the range. Recently I ordered an Apex trigger kit for the PC gun to get it up to the level of my other two 2.0 full sized M&Ps.
One other thing. I have read that the polymer frames flex more than a metal frame when the pistol is fired. That is said to somewhat reduce felt recoil. Can't say it's true, just read it on the internet.
Good luck with your pistol. An M&P sure does feel good in your hand and with an Apex trigger and good barrel they're tough to beat.