re: How were German armored divisions so much more elite than their US counterparts

The U.S. Army has a tradition of naming tanks after generals.

The U.S. had a history of building up for a war effort, then dismantling the war machine in times of peace.
Keep in mind, Germany had openly violated the Treaty of Versailles in the years that preceded the war. One of the caveats of which limited its military.
The US and allies eventually gained an advantage with numbers and maneuvering, but toe to toe, the Panzer was superior to the Sherman.