On some level, it's a lot easier to rationalize away slavery than it is the Holocaust. Someone might make the case that slavery was somehow a benefit to those enslaved (see: White Man's Burden), but it's kind of hard to argue that putting civilians in front of a firing squad is somehow beneficial to those so condemned. On another level, slavery didn't leave behind terribly much in the way of permanent structures. The Holocaust did. Beyond the myriad mass graves you also have the camps themselves. And the German governments both made a point to maintain them, both as a reminder and as a warning. You can still visit a fair number of them; I've been to Sachsenhausen.

Beyond that, the physical legacy of WWII is readily apparent. Aside from buildings deliberately restored, it's often difficult to find buildings that even look like they might predate the war in the big cities. Consider this shot of Berlin. The architecture bizarrely modern for a city that's been one of the seats of German power for centuries. With the exception of buildings deliberately restored so that they look prewar, it's a modern city. And, as an American (which I am), it can be easy to forget that cities in the Old World often feature an eclectic mix of architecture simply because they're so damned old. And even buildings that have a facade that could pass as pre-war often look nothing like that once you get inside. The Bundestag looks like it could pass for a set on a scifi film.

But, perhaps more than all of that, is the fact that we have an absolutely staggering amount of information available regarding daily life in concentration camps... and precious little regarding daily life for a slave c. 1850. We have photographs of civilians put in front of firing squads (and sometimes color footage of that), but photography was relatively new when slavery was still legal and we have precious few "candids" of slaves. The same can't be said of WWII, which broke out just a few years after Kodak came out with what was probably the first truly successful color photography system (color photography predates WWI, even, but it's relatively rare prior to WWII -- and even WWII has a lot of black and white footage).

And even if all of that weren't enough, we have mounds and mounds of other primary sources. War memoirs (Germany produced some truly superb war memoirs at this time), administrative records, newspaper accounts, and on and on. WWII is a veritable treasure trove of primary sources. The same often can't be said of early 19th century American slavery.

But what I suspect is the most important factor is that, after WWII, there was never any hemming or hawing. In the face of all the aforementioned evidence it was essentially impossible to plead ignorance, nevermind indifference, to the Holocaust. Germany was never let off the hook (nor should it have been), whereas the American South was just about given a pass -- note how the rhetoric from the Union was often about maintaining said Union, not about abolishing an irredeemable and inexcusable system of oppression. The fact that flying the rebel battle flag only became a problem recently is kind of evidence of that.

One reason is that though the United States ddi away with slavery in 1865, it did not permanently do away with institutionalized white supremacy. Though there was a brief period under military Reconstruction in which Southerners attempted to form racially equitable governments, the Compromise of 1877 rendered these moot, and returned widespread control of the South to white people. Many in the North, whether through racism, expedience, or a combination of those and other factors, found it easier to restore the nation on the basis of fellow feeling between whites. You see this in the rise in the 1880s and 1890s of mixed veterans' celebrations, in which the valor and bravery of both Union and Confederate soldiers was celebrated, despite the fact that Confederate soldiers quite literally fought in favor of both treason and slavery.

Once Southern whites were put back in charge of the South, they quickly instituted Black Codes, poll taxes and other Jim Crow laws which worked to limit the possibilities of newly-freed slaves. This is known as de jure segregation: The white majority used the law to maintain white supremacy. In the North systems of white supremacy also developed, though these were more likely to be de facto, including such practices as redlining and housing covenants, which were designed to keep black people from ever settling in a given neighborhood.

In Germany on both sides of the Iron Curtain, much of the reconstruction work was accomplished by outside powers. The Soviets and NATO were not as tightly bound by a sense of fellow-feeling or kinship with Germans, and so could approach de-Nazification somewhat more rigorously. Also, unlike the postbellum South, with its large population of freed slaves, postwar Germany had been essentially denuded of the groups of people whom the Nazis found objectionable. It's a lot easier to admit what you've done to the hated Other if you don't actually have to live with him any more.

Sources:

Blight, David W. Race and Reunion Foner, Eric. Reconstruction

I am going to disagree in part and agree in part with /u/Imperial_Affectation's post. I agree with the relationship between Holocaust remembrance in Germany and the evidence of the perpetration. What I disagree with is this being the primary reason for the German response to the Holocaust.

There are a myriad of possible reasons for Germany's acceptance of it's role in genocide. This acceptance certainly makes it an anomaly as a great host of other people's have refused to accept their own perpetration of genocide (Turkey, Japan, and to some extent Serbia fit this).

We can then analyze how these other states rejected or accepted their role in genocide to discover a difference in Germany.

First, lets look at photographic and other physical evidence. In the Bosnian Genocide and the Japanese atrocities in China, there certainly exists quite a bit of evidence. In the Medz Yeghern (Armenian Genocide), there also exist a number of mass graves that have been uncovered and studied. Yet in each of these cases, there seems to be a significant and purposeful denial of genocide by the people and governments. Hence photographic evidence of Japanese atrocities, graves of Armenian victims, and graves & DNA evidence of Serbian atrocities exist. There certainly is no room for denial in any of these cases. Yet, we see it. Therefore, we cannot assume that evidence alone is the reason for denial of atrocities/genocide.

Perhaps, instead, it is being the defeated state in the war during which the atrocities occurred? Again, evidence suggests that this alone is not the case. The Ottoman Empire was among the defeated during WWI, Japan during WWII, and Serbia during the Yugoslav Wars was certainly not victorious. Yet in each state, the education system and the government itself, fails to admit any sort of responsibility for the people (other than individuals in some cases) or government. Furthermore, in Japan and to some degree in Turkey and Serbia, new governments or new leaders were installed. Yet, in spite of a disconnect between the old government and the new, there still exists systemic rejection of war crimes or genocide.

In the cases of Germany, Japan, and Serbia, there were also war crimes that made clear the nature of the atrocities committed. In Japan, a great number were tried and convicted of war crimes. Additionally, in Serbia there were and continue to be such trials. In both cases, the stance of the government denies collective or state responsibility for the atrocities. In Japan, there is a denial of war crimes and in Serbia, there is the claim that it was individual action rather than that of leaders of the country. Clearly war crime trials alone do not make public or state denial of atrocities unlikely.

Let us also consider the economic realities. Is it possible that Germans were able to accept their responsibility because they were economically secure during the years following the atrocities? There are two arguments to be made that it was not this security that made Germans accept their role in the perpetration of the Holocaust. First, while Japan did not follow the exact same trajectory that West Germany did following the war, both were occupied by the US (and in Western Germany, France and Britain as well). This occupation resulted in rather amazing economic successes. According to the Maddison Project, by 1970, West Germany and Japan were the third and fourth strongest economies respectively. Hence, it cannot be that economic prosperity was the primary determinant in a people's acceptance or denial of its own atrocities.

What then might have caused this? I suggest that it was the geopolitical circumstances in Germany that created the situation in which Holocaust denial was an untenable position for a people or government. The nature of the German occupation (resulting in a split Germany) meant that neither Soviet nor Western Allied occupied Germany could embrace the events of the past as acceptable. Such acceptance would certainly tarnish the state and legitimize the rule of its counterpart. While both occupied states struggled to deal fully with Germany's Nazi past by dealing with individuals, they did make repudiation a state policy. This seems to have trickled down to the populace. Japan, on the other hand, did feel the full force of an even more rigorous occupation, but did not seem to have embraced the acceptance of its atrocities. This might be because its refusal to accept these atrocities fully did not compromise its status as an ally of the US.

GOOD READ This AskHistorians thread on NSDAP-like parties in post-war Germany.

Sources:

Rohde, David. "Denying Genocide in the Face of Science." The Atlantic. July 17, 2015.

The Maddison-Project, http://www.ggdc.net/maddison/maddison-project/home.htm, 2013 version.

Vogt, Timothy. Denazification in Soviet-Occupied Germany: Brandenburg, 1945. Cambridge: Harvard University Press, 2000.