While I have not fired either (maybe next time I am in the states), I can say that I would prefer the thompson on the single basis that it was so successful a firearm during WWII.
The M3 was designed not to be a better replacement gun, but to be a cheaper replacement gun.
If you know the firearm, you can control your rate of fire, any individual can put out a very effective fire radius out to 300+ yards.\
I don't mean to take away from the M3 in any way, but always remember, it was designed for a purpose, and that purpose happened to be a government that was looking for ways to outfit soldiers with effective and reliable firearms for far cheaper then the current array of weapons at the time.
It does not mean they are better then the Thompson, only different.
For Canadian shooters who go to the states and fire a few mags off, it is hard to get to know any gun with such a small amount of ammo.