"The Germans did not treat all prisoners from all countries equally." In what ways was this statement true?
I would say that is a very accurate statement. German policies towards their prisoners of war represented a mix of traditional Prussian views of honor and civility and the views of National Socialism and Hitler's racial beliefs.
Overall, American and British POWs were treated fairly. Being held by the Germans was no picnic, mind you, but the vast majority of said prisoners emerged from the war alive. The Germans also knew that their own soldiers were treated fairly by the United States and Britain.
Soviet and Polish prisoners were another story. Since Stalin did not trade for prisoners (He considered them dead. Stalin's own son died in a German concentration camp after his father refused to trade a high ranking German officer for him), the German Army suddenly found itself with hundreds of thousands of prisoners. This was both a liability in terms of resources and a drag on the military advance. Rather than construct new POW camps, Hitler simply fed many of them into his Holocaust machine and murdered them, after he had exacted a slave labor toll from them. This was also true for Poles, as Hitler regarded all Slavic populations as untermenschen, subhuman.
Allied air crews shot down over occupied Europe were perhaps treated the best of any POWs in Germany, held in separate camps and, unless they tried to escape, treated quite humanely.