Lets start off with the Soviet Union. Also know as USSR (Union of Soviet Socialist Republics) In Russian it's CCCP. The Red Army was the army known for the battle won in Stalingrad. What most Red Army soldiers worn was just about a coat for the winter, a belt with magazines and a rifle. The Red Army had millions of soldiers during the war and couldn't supply the soldiers that much. Especially since the civilians were being targeted from the Nazis and killed to cut off the supplies. Mostly every Red Army soldier looks the same. Uniforms regulations made the officers pretty much look like enlisted men even though they are a higher rank. The only thing significant is the Hammer and Sickle pin their hats. Representing unity of peasant and workers.
The United States military became aware that warfare was changing. The old approach of formation lines was no longer a viable way to fight. That's what made the US uniforms change a lot to the new warfare of World War 2. The Beginning of the war for the US wasn't very good though. They mostly used the same uniform and equipment from World War I. What the US were good at was camouflage, especially for the Marines in the Pacific. Their uniforms that the US wore in the Pacific were camouflaged to the environment the Marines were fighting at. The only thing significant about the uniforms on the US soldiers during battle was the ranks and patches in their uniforms. it represented what branch, division or infantry they were in. The most famous during the war was the 101st Airborne Division. The famous patch they wore was the screaming eagles/. But on their dress uniforms they wore ranks and medals that they have earned during or after the war.
The best uniforms worn during the war, has to be the Nazi SS Soldiers. These SS uniforms were tailored to project authority, and foster fear and respect. As Himmler put it, "I know there are many people who fall ill when they see this black uniform; we understand that and don't expect that we will be loved by many people". These uniforms were made for authority and respect for the nazis and german soldiers. But its was for fear to the enemy of Nazi Germany. Some special little details are the pins in the uniforms. The most important is the "SS" pin in their collar. It represents two lighting strikes to represent that they are the most elite soldiers. Also in their Visor hats you can see they have a skull insignia. The skull of that Nazi SS insignia appears, also known as the death's head it represents loyalty unto death.