Most Western Front air combat took place at altitude because of the bombing campaigns. The bomber formations were coming in at higher altitudes for more efficient flying, and thus interceptors were coming to these altitudes to fight and any escort fighters were going to be operating at similar altitudes to the bombers they were protecting.
On the Eastern Front, however, the dynamic was significantly different. The air war was far more tactical in focus, and a variety of factors came together to push engagement altitudes lower. Heavier reliance on light bombers and attack aircraft meant typical targets for fighters were flying much lower. The dive-bombing tactics the Luftwaffe was famed for were more of a medium-to-low-altitude method, and their later shift to using Fw 190s in attack roles would see the fighters make high-speed, low-altitude runs to sneak in through early warning networks and outrun enemy fighters at low altitudes. The famed Il-2 relied heavily on guns and rockets for its attacks (as its payload of bombs was relatively small), and thus required fairly close approaches that kept the aircraft at low altitudes. Even the Luftwaffe's heavier bombers did a fair amount of low-altitude operations early in the war in the East, with Ju-88s hastily co-opted to provide close air support in some instances and regular patrols behind the front to hunt down Soviet trains. Note that the nature of operations also played a part. While the strategic bombing campaign in the West was against very large targets - factories and industrial districts in cities - targets in the East were smaller and more tactical in nature. More advanced bombsights and bombing techniques in use in the West made high-altitude bombing of these large targets viable, while the lack of such in the East meant that bombing at high altitude was going to be too inaccurate for most operations.
For the Soviets, there was a major technological limitation as well, as they struggled to produce a viable supercharger (something absolutely necessary for high-altitude flight with piston engines) through the entire war. Though the MiG-3 was designed as a high-altitude interceptor, its performance wasn't spectacular even at altitude, and it was outclassed at the medium-to-low altitudes it ended up fighting at. When Lend-Lease began to arrive, the Soviets would ultimately rely on Lend-Lease Spitfires and P-47s to provide what little defense against high-altitude threats they needed.
That's not to say higher altitude operations didn't happen. The aforementioned Spitfires and Thunderbolts were kept in service (despite the Soviets not being a fan of the aircraft close to the front) to counter German Ju-86P high-altitude reconnaissance aircraft, which were capable of operating deep in the Soviet Union at very high altitudes that existing Soviet aircraft were incapable of reaching. The early-war Soviet retaliatory air raids on Germany also took place at higher altitudes, although such raids had little impact.