As my Forum name indicates, I own some of each. I have an M&P 40 compact (v1.0) with 12,500 rounds through it. It is my primary carry gun. I also have a P320 compact which has 4,500 9mm rounds through it, and 3,900 .357 SIG rounds through it. I recently rented an M&P 40 4.25" (v2.0). and put 50 rounds through it, so I have that to compare as well.
Reliability: Both my P320 and 40c have been extremely reliable. Between the the two calibers, my P320 has had three failures to eject in 8,400 combined rounds. It will shoot any ammo I feed it. My 40c had one failure to feed, and three FTEs in the first 8,500 rounds. At that point, it started to have light strikes, which earned it a complete overhaul (free) by Smith & Wesson at 10,000 rounds. Since then, I've had only a couple of failures to feed, in each case caused by limp-wristing during one-handed shooting. Like the P320, my 40c will shoot any ammo I feed it.
Accuracy: A virtual tie. In my hands, they are both very accurate out to 20 yards. Although the P320 has a slightly longer barrel (3.9" vs. 3.5"), at 20 yards I'm equally accurate with each. I am more consistently accurate with the 40c, most likely because I have shot it so much more. I've shot them at 25 yards, but my accuracy deteriorates so much with both that I haven't shot either one very often at that distance.
Trigger: Hands down, out of the box, the P320 wins by a huge margin. My 40c's M&P 1.0 trigger was initially awful, with a long, gritty take-up. After 1,000+ rounds, it smoothed out considerably, lightened up a bit, and became pretty decent. My P320's trigger was excellent from the first pull, and it's only gotten better since last year's upgrade, which is now standard on all new P320s. My P320's trigger is very smooth, has almost no takeup, breaks easily at (I'm guessing) 5.5 lbs, and has a very short reset. The trigger on the M&P 2.0 that I recently tested is closer to the P320's than the 1.0, but it is still not as good. The 2.0 I shot was fairly new and not fully broken in, but in comparison to my P320 and 40, its trigger, although smooth, was much stiffer (higher pull weight) than either of my guns. Take-up was shorter than my 40c, but still longer than my P320. The 2.0's trigger is definitely improved, but still is not in P320's class.
Intangibles: The ability to change calibers and sizes while using the same fire control unit is a big plus for the P320. I got bored shooting my 9mm P320 (9mm is boring!), so I converted it to a .357 SIG (.357 SIG is FUN!) using one of SIG's Caliber X-Change Kits, and I haven't looked back. That's harder to do with an M&P, and you can't use a factory barrel if you want a .357 SIG conversion. On the other hand, you can't beat S&W's lifetime service policy. Although my P320 has not required any factory repairs, SIG does charge for replacement parts (like recoil spring assemblies) that S&W sends you for free. If you want a safety on your gun, M&P is the only choice. The P320 has zero safeties, unless you count the recently added "drop safety" that was added as part of the trigger upgrade program. That, combined with a light trigger pull and very short take-up, makes the P320 too risky for me to use as a carry weapon. It's simply too easy to fire. That's why I chose the 40c to carry, and I've never regretted it. As to quality of construction, both my 40c and P320 are stoutly built and have run superbly. If my early model P320 is loaded with shoddy Indian "MIM" parts, it has not been apparent to me in its first 8,400 rounds. Any manufacturer can make a clunker now and then (Ask me about my Shield 9. No, don't.), but as far as I'm concerned, both S&W and SIG have delivered what they promised with these guns.
I hope this helps you with your decision.