Battlefield causality rates are examined in the book A War To Be Won in a context that's related to your question. In that book the authors note the high casualty rates of the Germans and the Soviets and compares them with the comparatively lower rates of the Americans and British. Their determination was that democratic societies could not afford to fight in a fashion that would result in casualty rates that high, and therefore they chose other methods of fighting that resulted in lower casualties. I'm sure that there's more to it than that, but their point is convincing. Max Hasting's book Inferno (if I recall correctly touches on some similar points.
Generally, in looking at this, the authors argue (in the first book) that the democratic allies took fewer battlefield risks but also emphasized technology and weaponry to compensate for simple expenditure of human life.
Looking at this from a different prospective, but perhaps a supporting one to this thesis, a book of the SS I've read, but I'll have to locate when I have the chance as I can't recall the title, claimed that the SS (but not the Heer) purposely took high casualty rates to bloody their own men. That sounds extreme, but if you read the U.S. Army's post war history of German cavalry it quotes from SS sources to the effect that the SS expected the post war Frontier with Russia to be one of perpetual low level combat which would serve to do just that, and hence install combat virtues in future generations. That takes us somewhat off topic, however.
Can you get a little more specific? Are you talking about Germans taking heavy casualties in battles against Americans? Or just that generally throughout the war Germans took heavier casualties than the Americans did?