The Thompson was like a squirt gun, very controllable, high cyclic rate.
The M3 had a gawd-awful heavy bolt that slammed back and forth, jerking the gun all over the place. Rate of fire was quite low on the one I fired, which may have been due to a tired recoil spring.
Having fired both, would take the Thompson in a heartbeat.
From my extremely brief readings, the bolt was made heavy to slow the rate of fire. Should a bunch'a these be made public, a bolt replacement could "straighten" things out.
Yes, The Thompson has the edge in accuracy with a longer sight radius, more weight for control, and sights which could be set for various distances.
My brother produced a YouTube vid about the differences between the Colt 1921 model Thompson and the much more common 1928a1 model.