Including POW deaths, the Soviets had 10.6 million dead/missing, and 1.6 million living POWs, for a total of 12.2 million irrecoverable losses. Compared to the Axis (excluding Soviet collaborators pressed into service- so just counting the ones who died fighting rather than being captured), there were 7.3 million Germans killed/captured/missing. Factor in the other Axis allies (just subtract POW deaths from the POW numbers, and then add that number to the total deaths number), and you get the following irrecoverable losses:

Axis: 9,118,000

Soviet: 12,200,000

This can be further confirmed by comparing Soviet to German casualties after the first few months. No one really has any doubts that the German army invaded and surprised the Soviets who did not prepare for war. But if you take 1941 out of the equation and just maintain that the Soviet army from that point was comparable or superior to the German one, things start looking a lot different. The Soviets had over 3,600,000 men killed or captured during the first six months (Operation Barbarossa), while the Germans had 235,000 irrecoverable losses (186,452 killed, 40,157 missing, 11,000 captured) in the same period albeit with a proportionally high "wounded/crippled" figure. Which means, from late 1941 to 1945, irrecoverable losses were:

Axis: 8,830,000

Soviet: 8,600,000

However, Germany did not fight alone. The Axis Minors fought with them, and adding up only Hungary, Italy, Romania, and Finland adds another 1,725,000 casualties to the German side.

This isn't even adding the Japanese soldiers that died or got captured during the Manchurian operation

Also it is important to state that the Soviets spent most of the war on the offensive which is more costly in equipment and manpower