One of these combinations I can speak to is the German preference for the PPSH-41. The Russian winter was extremely harsh, especially on German equipment. The Russian equipment was oftentimes designed for those cold tolerances. The firepower and greater cold weather reliability of the PPSH-41 made it popular among German Troops.

Under such circumstances the PPSh-41 (known to its users as the 'Pah-Pah-Shah') received virtually no maintenance or even any cleaning. Under Eastern Front conditions it soon became apparent that the best way to keep the weapon going under summer dust or winter ice conditions was to keep it completely dry and free from any sort of oil, otherwise its action clogged or froze. So many PPSh-41 submachine guns were produced that the type became a virtual standard weapon for the German army as well as the Red Army, the Germans even going to the extent of recalibring some of their captured hoard to their own 9-mm (0.354-in) Parabellum cartridge: this process required the replacement of the Soviet barrel and a housing able to accept the magazine of the MP 40. Unaltered weapons in German service received the official inventory designation Maschinepistole 717®, but the designation of recalibred weapons remains unknown. Partisan forces operating behind German lines found the PPSh-41 an ideal weapon for their purposes, and after the war the type was used by virtually every nation that came within the Soviet sphere of influence. It still turns up in the hands of 'freedom fighters' all over the world.

Source: The Encyclopedia of Weapons: From World War II to the Present Day

As a follow up here how common was it for combatants to use the other sides weponry.