While 'the winner writes the history' is true to some extent, I'd argue that the Soviet Union were the lesser of two evils.

Nazi Germany killed about 5,5 million jews and 8-10 million others (roma, homosexuals, socialists, communists, handicapped people, Soviet and Yugoslav POWs and civilians and so on) by death camp, einsatzgruppen, executions by the military and deliberate starving in concentration and POW camps. Another 10-20 million were killed as well, mostly Polish, Yugoslav and Soviet civilians. A vast majority of these deaths happened between June 1941 and December 1944.

As a comparison, Stalin's crimes, if you disregard Rummel's and Conquest's demographic based data (of 30-60 million) totals up to between 2 and 6 million dead, plus another 4-5 million dead in famines, which can be argued wether it was a directed policy to kill people or just criminally incompetent economic policy.

Ellman writes:

The number of deportees (first peasant victims of collectivisation and then mainly the victims of ethnic cleansing) seems to have been about 6 million. Currently available information suggests that the number of those sentenced on political charges was also about 6 million. If these two categories are deemed asthe ‘victims of repression’ then the number of the latter was about 12 million. (Of these, from 1921 onwards about 3–3.5 million seem to have died from shooting, while in detention, or while being deported or in deportation. In addition, a currently unknown number died shortly after being released from the Gulag as a result of their treatment in it. Furthermore, a currently unknown number were killed by the Bolsheviks in 1918–20.)

It should be noted that the latest research comes from the opened NKVD archives and their own bookkeeping.

Stalin's terror numbers emerge around 1 million directly executed, but there were a policy of "pardoning" those in the Gulags that were ill and about to die, so they were registered as natural deaths while the Gulag was the direct source of their death.

Even if you use

The atrocities of the Nazi's was more easily accessible first, you have the allies on the western side parading the horrors and the soviets in the east doing the same. The soviet atrocities were far less accessible because you have an intact regime under Stalin that was big on the strict control of people and information, so immediately you have subjugated areas who aren't forth coming about what's happened to them.

Another prudent factor is the tensions between east and west over Germany and the very real potential of continued war which not too many people were up for so it was better to relish victory over 'Evil' and ignore the elephant in the room to prevent a further call to arms. This further constrains information flow early on.

Its already been mentioned in part, but due to the fact that the territory the Soviets attacked was largely under their sphere of influence for five decades, with limited Western interaction, it was not as publicised as the territory the Nazis took over, which largely composed "the West." Once again, I will cite Timothy Snyder's Bloodlands: Europe Between Hitler and Stalin, as he provides the very same argument. This can also be seen as more Soviet-era archives are declassified and opened up to Western historians, who are now publishing their findings and letting the wider world understand what happened in that part of the world.

Specifically, which crimes are you speaking of?