You are quite correct that this is one of several training films that were made it's a way if trying to prevent US soldiers from being intimidated by German weapons, especially the MG42, sometimes called "Hitlers Buzzsaw" which had a rate of fire about twice that of the equivalent US machine guns of the day, the m1917 and m1919. I'm betting that the guys over in /r/guns would love to take a crack at this but I can offer a few comments. As someone who has worked in the propaganda (advertising and marketing being the civilian term) these films fascinate me.

1.) The Thompson has a slightly higher rate of fire then the Schmeisser, I believe 700 rounds per minute vs about 500 for the Schmeisser. Not a huge difference but still something. They both had similar magazine capacity, 30 rounds for the Thompson and 32 rounds for the Schmeisser. The Thompson was obviously much heavier, which is not necessarily a bad thing who you consider the size round it uses. The shmeisser was lighter and cheaper to make, which can have some effect on how easy it is to damage in combat but overall both had reputations for being pretty rugged. The M3 was intended to be a cheaper alternative to the Thompson, using the same .45 Acp round but much lest costly to produce. However, it did not see much action in ww2 compared to the Thompson so it's effect on the battlefield is negligible. The.45 and 9mm rounds are both very accurate rounds in the hands of someone who knows how to use them. When fired from sub machine guns they both have similar effective ranges although the .45 is going to have more kick, making a gun chambered for that round a little bit more difficult to control. But again that is where the thompsons extra weight can help. The .45 is also going to have more knockdown power then the 9mm although the 9mm is no slouch either. There are arguments both ways which is actually the superior weapons but in response toy our question yes they did have similar rates of fire and accuracy.

2.) the machine guns are also an interesting and debatable comparison. The Germans were chambered in the classic 7.92x57mm Mauser, commonly known as the 8mm Mauser. American machines guns mostly used the 30-06 also commonly known as the .30 caliber or m2 ball ammunition. They are similar size rounds with similar performance although the 30-06 is generally seen as a little better overall. But if you consider that both are still used in hunting and sporting to this day, that says something about their quality. The big difference between the American and german guns was the rate of fire. Mg42s were just insanely fast compared to the .30 caliber guns. The thinking was that in combat you only get a limited amount of time to fire so why not make sure you are putting out as many rounds as possible in that window. Aside from needing to carry more ammo to support the increased rate of fire there is the possibility of heating up and burning out the barrel on the mg42. But this was usually prevented by the ease that the barrel could be changed out on the mg42. A competent machine gun crew could change out the barrel as fast as they could change to a new belt of ammo. In terms of accuracy, machine gunners are usually trained to fire in short bursts so that they can "walk" the rounds onto the target and keep the gun from getting ou to f control. Obviously a gun with twice the rate of fire is going to take a little bit more control to limit the bursts to 3 or 4 rounds. If you notice on the film the .30 caliber guns were being fired in short bursts, while the german guns were being given much longer bursts, or with the mg42 it looked like pretty much one long burst. Soooo of course the german ones were a little less accurate.

So in short, good questions! And I know there are people on here with pretty significant knowledge about the specifics in the ammo and all that. I do love these old training films, they are classic examples of American propaganda.