There's 37mm and then there's 37mm. The cannons Rudel used were BK 3,7's, which fired the 37x263 belted round. The M4 in comparison used the 37x145 rimmed. They were not in the same ballpark in terms of power. Even the BK was marginal for this task by the time it was brought into service as such. Rudel got away with it because he got very close before firing, knew the weak points to aim for, and was a very good shot. He also did not get all his tanks with cannon fire; divebombing was still the preferred way to do this and was much more successful overall. We remember him for the big guns today but it was his skill at bombing that earned him his fame back then.
He was also quite aggressive, which must have played a role in his numbers. It's been a while since I've read his book but IIRC he rarely came home without a shot-up aircraft and was actually brought down a number of times, losing at least one tailgunner in the process. I do remember him mentioning firing from inside 100 meters for maximum effect -- not an activity for the faint of heart.
Interestingly enough, Rudel did report that the Stuka G's were fantastic for screwing up water crossings. The Russians tended to use a lot of crude barges built on site; most aircraft weapons would simply drill a lot of holes in them and cause some swearing, but the boats themselves would often stay afloat and if they sank, the crew could get out and swim. The BK's were directly descended from Flak 18's and used the same ammunition, which was still in the inventory; loaded with HE projectiles, such boats (and presumably their contents) could be completely demolished in a single hit.
As far as anyone can tell, the Russians never used the M4 in an antitank role. With the proper M80 AP loads contemporary tanks would've only been annoyed by it, and the US never sent them any AP ammunition. The HE loading would've been ineffective against even most prewar tanks. There's some confusion about what role they played in attacking softer ground targets as reports differ, but it's generally agreed that if they were used as such, it was secondary to dealing with other aircraft. It should have performed adequately at this role though -- heavy armor, good low speed maneuverability, plenty of firepower and no exposed cooling system. I suppose that it would take a certain kind of pilot to roll like that without an engine between himself and incoming fire, though.

There is a reason that radials are remembered as the engine of choice for mud movers.
If 30 rounds was light, the Stuka's BK magazines held a mere twelve rounds. That's not a lot of shooting, but compared to a bomb-armed Stuka acting as a divebomber there was the potential to destroy more tanks at less cost. It made sense from a commander's standpoint, I guess. Remember that both of these guns were originally designed to perform a very specific role, and that even
one success would justify the expenditure of the entire ammunition loadout. Lots of ammunition was not required -- was not even possible, really.
As for the Finns, BW-393 is the plane thought to be the most "winningest" airframe of WWII, with 40 victories achieved in it. The Brewster is one of those odd planes (like the P-39) that is remembered today as being inadequate, when in reality it was simply used incorrectly. As has already been stated, the Finns did great with it and loved it. The Allies considered it to be a widowmaker and did not do well with it. Why?
Simple -- the Americans had wanted a carrier plane and set it up as such. It was not a good choice for this. When the Finns received theirs they had no preconceptions about what it was supposed to do and simply fixed it: excess armor and baggage was removed, the weapon loadout was changed slightly to something that made more sense, and the maintenance issues with the engines were figured out and corrected. (Rather simply, at that.) The underpowered dog became a fast, agile fighter, and then the Finns (with a little help from
Hans Wind) figured out how best to fly it, instead of figuring out how best to make it fly like they wanted to fly as the USN did. Between this and the very different nature of the air war over Finland from the Pacific theater, they wound up with one of the most successful aircraft of the war.