This is a very big question, that academics have written a lot of books about. I'll try to answer it short and concise. The sources, that I would recommend reading yourself, would be Buruma's "Year Zero" and and Münkler's "Die Deutschen und ihre Mythen". Otherwise it wouldn't be a problem finding other reliable sources.

So firstly, there was a big difference in how the two countries handled the former history of Germany regarding the nazi past. In the case of the DDR, this handling has to be understood in the light of both Soviet and German communist activites in the interwar period. Summarized, these movements were against the rise of national socialism, which gave them the opportunity to say that they had always been against nazism. This was not the case in BRD, as they couldn't credibly call themselves communist resistance fighters without jeopardizing their new ties to the former Allies.

So let's treat the countries separately. Firstly the BRD. In the BRD, there were thourough tries by the Allies to put the former nazis to justice, something that failed because of several factors. The main way the Allies tried to do this, was by giving Germans questionnaires where they themselves were supposed to fill in the blanks regarding their whereabouts during the nazi era. Understandably, people then lied and vouched for each other. The great majority of supporters for the nazi regime was suddenly reduced to a small minority. This of course made the denazification of the BDR a lot harder, as they wouldn't know who to target. Secondly, the Allies and the BRD quickly realized that the people they needed to rebuild the country were exactly the people that had been having administrative (and other) positions during the Nazi era. At several points in the years following the war, you had a lot of former nazis sitting in important positions (for a light read: https://www.businessinsider.com/former-nazi-officials-in-germany-post-world-war-ii-government-2016-10?r=US&IR=T).

This didn't really change until the youth-revolt and the Frankfurt-Auschwitz trials of the early 60s, when there was once again attempted to get clarity concerning who did what during the nazi era. A lot more successful this time. Once again, this was only made possible because of the distance gained to the existential view of history following the war (See Klas-Göran Karlsson's typology of use of history).

In the DDR though, they could afford being a lot rougher with the former participants of the regime, because of the identity they forged as resistance fighters. This resulted among other things in the DDR claiming that Buchenwald was liberated by communist inmates, rather than by Americans. A different, but still interesting subject I would recommend you to check out. Secondly, they were to a great degree run administratively from the Soviet Union, which removed the middle link between the victors and the german people that you had in the west. So the people in the east, who a lot more thouroughly were vetted, who didn't pass the test, were imprisoned and barred from all influential positions. So far, no big difference with the BRD, but here the constructed identity of the DDR kicked in.

The BRD on it's side, saw the need to acknowledge and process the national socialist past, as they recognized the fact that it had permeated every layer of society. In DDR this never happened, as they stayed with the idea that this was a case of us (the communists) versus them (the nazi collaborators). This can also to a degree explain the different popularity of right-populist and neo-nazi parties in the western Bundesländer and the eastern, as the horrors of WW2 never were blamed on the germans per se in DDR.

So that would be a very short summary of a historical fact that deserves a lot more attention. Please ask if you have any further questions.