The PPsh-41 submachine gun had a lot of advantages over the German MP 40. But namely: It was cheaper, faster, and easier to manufacture. Because the bullet diameter was the same as the Mosin, 7.62, the PPsh-41 was made using a cut-down Mosin barrel. One Mosin barrel = Two PPsh-41 barrels. Cleaning was easier because of the hinged receiver, important during times when regular maintenance might be difficult. They made 5 to 6 million of them during the war.

It wasn't the most accurate firearm but the high rate of fire combined with the huge (but heavy) 71 Rd drum made it hard to miss. The Soviets weren't against issuing the gun to entire companies! Even the Germans would use the gun, it got a Heer designation: MP 717(r) or MP 41(r) for ones converted to 9x19mm. The Germans could issue the MP 717(r) with their own ammo, 7.62x25mm Mauser. Same size, but not as powerful as the Soviet 7.62x25 Tok. They even issued German manuals for the firearm. (Side note, never feed a 7.62x25mm Mauser firearm Tok ammo. You're liable to blow the gun up.)

The Germans had a tendency to use captured Soviet arms and giving them Heer designation. The Soviet TT30 pistol was called the Pistole 615(r), and the SVT40 semi auto rifle the G.259(r). It also went on to influence the design of the German G43 semi auto rifle. I'm getting off topic.

By comparison the MP 40 saw about 1.1M units produced. The MP 40 was a similar war-time production gun though. Both made heavy use of stamped metal parts which reduces cost and time. They could be made by unskilled labour. After the Nazis ran up against entire companies with PPsh-41, they started to issue the MP 40 on a limited basis to assault companies to try to meet the volume of Soviet fire. A lot of the Urban fighting, like the infamous Battle of Stalingrad, really highlighted the problems with rifles. They were accurate, but made for fighting at 500+m. When most everyone is getting shot within 300m or less, you start seeing the advantages of cheaper, shorter-range firearms chambered in pistol calibers. The weight of fire compensates for the lack of range and accuracy.

In the end though, both were cheap to make, both were refined from more expensive designs. Both firearms had a problem with feeding due to magazine designs. The Soviets made more though, and their use made the Germans reconsider their own doctrines concerning automatic small arms. The PPsh-41 had a higher rate of fire and supported larger magazines. It was also a select-fire weapon, while the MP 40 was a full-auto only (albeit slower). The MP 40 was lighter and shorter because it opted for a folding stock.

The weaknesses of the PPsh-41 aren't uncommon in it's contemporaries either, like the British Sten, American M3, and German MP 40. They're all stamped-steel guns, but the M3 and Sten were both influenced by the German MP 40, while the PPsh-41 was influenced by the Finnish Suomi KP/-31. All of them were fairly cheap to make, and were made to replace more expensive and labour-intensive firearms. All of them suffered from problems with their magazines.

Personally, just by sheer production volume, rate of fire, and magazine capacity the PPsh-41 is a beast compared to the MP 40. It was a damn bullet hose, and coming up against an entire company raining fire on you? Damn. It's not hard to see why the Germans took as many of them as they could.

Source: Chris McNab, Soviet Submachine Guns of World War II

edit: details, words, naming consistency

Mosin Nagant vs. K98:

In effect, these rifles were functionally identical for both sides throughout the war. Both fired a full-sized .30-cal cartridge with an effective range of 600ish meters, both have 5-round internal magazines, both take a bayonet, both are bolt-action rifles.

The Mosin has a slight edge in longevity/durability in awful conditions, simply because they were designed to operate with special lube during winter months. There are plenty of reports of German equipment (rifles, machine guns, trucks, etc) locking up in the cold because their lubricants froze. Soviets didn't experience this as much.

The German K98k is hands-down a better built rifle, and across a sample of 10 or 100 rifles, you'll notice that the K98's are more inherently accurate; this is due to more consistent manufacturing techniques, parts being machined to tighter tolerances, and the parts having smaller clearances when fit together. Mosins are a little more "crude", and it shows. You can see a lot of obvious tool paths, machining marks, on wartime 91/30's.

Both are strong, both are tough, both will kill you dead, but I would give the edge to the K98 in most categories. It's just a nicer weapon, and has the benefit of being shorter (easier to handle) and slightly lighter. Both use open-leaf tangent sights with a hooded front post, both take a bayonet (Mosin's is much longer), and that's really about it.