At Kasserine, El Guettar, in Sicily, at Salerno, in Caretan, Lehr in front of St. Lo, Mortain, the early Lorraine fights culminating in Arracourt, the Bulge, and Alsace. In the largest of these, the Bulge, the US lost 2 divisions. In Kasserine it was 2 regiments. In most it was more like 2 battalions, and in all cases these initial losses were 2 echelon levels smaller than the German attacking force.
And those were inflicted precisely by having better odds (especially in armor) at the initial point of attack. As soon as US reserves arrived and redressed that, the Germans started losing. Read in particular the story of US third army in Lorraine in September, in Hugh Cole's "Lorraine Campaign" (one of the US army "greenbooks", the official history).
The Germans did have pro officers, excellent infantry that fought very hard, and superior tanks. But they had very stupid high command, an overly aggressive doctrine that threw away their armor on fruitless counterattacks, and not much in the way of mobility as an entire force. (80% of the army was rail and horse dependent). On the east front their "play" in pure military "chess" terms was quite poor from the autumn of 1942 on, with only passages of brilliance. Anyone who can read a map can see the Russians made better moves at the top level.
Also, the Russians beat them in the home front stuff on their own. From the same industrial base prewar and under far worse conditions (the Germans took 40% of the country's population and industry), they outproduced the Germans 2:1 in tanks. The reason is the Germans were so arrogant after their early cheap victories over lesser opponents, they didn't bother to mobilize their economy when they attacked Russia. This is one of the great world historical blunders. And that one was entirely an "own goal", pride as a weakness.
Wasn't there a quote from Patton to the effect that "the worse the infantry, the more artillery that was needed, and the US infantry needed a lot of artillery"?
On the east front their "play" in pure military "chess" terms was quite poor from the autumn of 1942 on, with only passages of brilliance. Anyone who can read a map can see the Russians made better moves at the top level.
The war was over in winter of 1941 when the Germans failed to take Moscow or the Russian heartland behind it to Novgorod and Sartov and Volgograd. That plus the Urals and the near west of Siberia equalled enough human and natural resources to eventually defeat Germany.
(the Germans took 40% of the country's population and industry)
Much of Russian industry had been relocated from the Ukraine to the Urals as a precautionary measure by Stalin. Much else was uprooted on the spot during the invasion and sent east along with around 15 million people. The Germans didn't find all that much to work with, and spent an enormous amount of resources rebuilding Ukrainian industry in the 1942-1943 period, only to immediately lose it.
The reason is the Germans were so arrogant after their early cheap victories over lesser opponents, they didn't bother to mobilize their economy when they attacked Russia.
They didn't need to. German war theory was based on the quick victory of the Blitzkreig. Had Hitler struck Msocow in August/September of 1941 after the taking of Smolensk, rather than making his Ukranian diversion, the war likely would have been over by the winter before the US entry, since the Russian nerve center would have been taken. Its quite obvious Germany could not win a war of attrition against Russia or the US. The German war plan against Russia called for a lightning strike and the occupation of Moscow within 12 weeks, with a solidification of a front line against remnant Communist forces on the axis of Arkhangelsk-Astrakhan along the Dvina and Volga rivers by early winter. A number of military historians, such as Gen. R.H.S. Stolfi ("Hitler's Panzers East") have pointed out how this campaign would have succeeded had it not been diverted by Hitler right at the moment of impending victory.
Again, Germany could not hope to win a long war of attrition against the US or Russia because of superior resources in the hands of those two countries.