I have the M&P 9 full size and the 40c. When I got home last night I mic'd the barrels. They are exactly the same in respect to chamber width and length as well as barrels thickness (outer diameter) The only diff is the .40 has a thinner barrels (inner diameter). I placed the 9mm barrels in the .40 slide and it locked up tightly. I was able to chamber and eject a round easily as well. I would not shoot the weapon with the full size barrels on the compact frame, but will be buying the S&W 9c barrels.
I just recieved my S&W M&P barrel from Brownells. Cost was $75.00. It was just drop in and go. I was able to use the 9mm mags from my M&P full size. After making sure I was able to work the slide without any trouble I chambered and ejected 15 rounds without a hitch. It was now time to shoot it.
This is a group with the 40 S&W at 10 yards. 8 shots (only 7 in the target)
Switched to the 9mm barrel. 8 shots at 10 yards.
While I will never tell anyone to do the same as I did, I have to tell you how well it worked for me. I then went on to rapid fire over 100 rounds as rapidly as I could. I never had a malfunction of any kind.