The M&P2.0 Compact was introduced to compete directly with the Glock 19.
The biggest difference between the M&P2.0 Compact and the SIG P320 Compact is that the SIG P320 is a little taller, and a little fatter, and it does make a difference. I tried the P320 Compact, and it is noticeably harder to conceal than a G19. Small differences really do add up. The G19 hits a "sweet spot" of size, capacity, and shootability that no other make has been able to match. The P320 Compact is simply not as concealable as the G19.
The M&P2.0 Compact, on the other hand, is the same size as the G19. That said, the sandpaper grip on the M&P2.0 Series is just not good for concealed carry for me, and I have seen others make the same criticism.
So, were it me, I would opt for the G19 over both the M&P2.0 Compact and the P320 Compact.
In addition, the SIG P320 is under a "voluntary upgrade" now as a result of the pistols discharging when dropped. If you get the P320, be sure you get an upgraded one. I am still not confident that the fix by SIG will prevent such discharges, and I am waiting for the You Tube tests of the "upgraded" P320 which I am sure people will do at some point. SIG, of course, had a bunch of people out to their facility to let them observe testing of the P320 after retrofit, but the drops were not from a very great distance, and they only did 3 drops, if I recall. I hope it works for them, but I'm skeptical.