The M-3 series was called the Grease Gun, even by us. It was a decent design, and worked well for the bullet hose it was meant to be. Machining could at times be inconsistent, a friend who owned a few of them, showed me the screw on barrel in .45 acp and a bullet just slid down, and out the muzzle. this didn’t stop it working mind you, but for 10 bucks I guess one can’t be choosey. 
They were also produced in 9mm presumably for Lend lease. These were not fool proof, if one was not careful, one could shoot ones self without a lot of trouble. I should have bought one while they were still inexpensive, a few hundred dollars.
So, in WWII do we pretty much have the Sten / UK, M-3 / US, and Owen / Australia as more or less equivalent in purpose if not necessarily reliability?
I’m excluding the Thompson as it was used by all those forces to varying degrees and filled its own niche in the armoury.
Sounds about right, everyone decided to go the “Cheap, Fast, and Dirty” route for such types of weapons. And don’t forget the Reising, (US) it was nearly as pretty as those you mentioned, and no one much liked them, I think the U.S. Marines were made to use them, and they always get the runt of the littler when it comes to any kind of weapon. In the 70’s a useable Reising was $50-$65. (Plus the $200 tax on the transfer) Not very popular, even among Civilians. 
I thought it was relatively simple to change the calibers between .45ACP and 9mmP?
I watched a change over, a different Bolt assembly, Magazine, and Barrel, and all done. Took only a couple minutes. The danger in the M-3’s were that the Bolt didn’t need to go back far enough to catch the sear in order to strip a round, and chamber it. Which motion also fires the cartridge as the firing pin is fixed. Unless one has the cover closed, jumping down from a truck, or fence would be enough to cause the Bolt to slide back enough to fire a round.
I found this video of the M-3 being run, be sure to watch for awhile it isn’t just guy after guy running out a magazine.
And if you’re interested in the Thompson, see it here.
And the Owen SMG.
And the Venerable Sten…
Here is a video on the use of the Liberator Pistol using one of the new made reproductions.
https://youtu.be/_ERSQo6cmTQ
My Father, who fought in the Dutch underground during WW2, was attached as a scout to a Canadian unit in Holland at the end of the war. He told me in passing that the Sten had the unfortunate tendency to fire seemingly spontaneously. He had one and wasn’t too thrilled with it.