"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.