It is a rather difficult question to answer.

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For one, the US Army and the Wehrmacht were constantly changing beasts during the war.

You must also look at the context and location in which armies are fighting, really.

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As it stands, if the UK and USSR did not fight, then you can assume that the Wehrmacht controls just about all of Europe, with a very experienced army that won rapid victories against Poland, France, Denmark, Norway, Greece, Yugoslavia, Netherlands, Belgium, Luxembourg, with the rest of Europe either being neutral like Switzerland/Sweden or one of Germany's allies or satellites, like Italy, Romania, Hungary, Finland, Slovakia, Bulgaria.

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In this scenario, where do they fight?

The US has no toehold in Europe. They'd have to supply an invasion force from the US itself, unless they were willing to invade a neutral country as a staging area, which isn't exactly easy in itself and probably gains Germany some allies. D-Day was very difficult to plan and execute, and this was with massive numerical and material superiority against an exhausted depleted Germany, while only having to cross a very narrow English Channel in the space of a day.

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Invading Europe from the US would see the Americans crushed, because maintaining supplies would be incredibly difficult, not to mention the Germans would have an overwhelming air superiority since the Luftwaffe has not been depleted by the Battle of Britain, the Eastern Front, or the defence of the Reich. The only planes the US could bring to bear in Europe would be carrier based, which would not be enough to fend off the thousands of planes that Goering would throw at an invasion fleet that would absolutely be detected way ahead of time, judging by the distance it needs to cover and the number of ships required.

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Invading the continental US would have been impossible for the Germans as well.

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So, it is difficult to imagine a scenario in which the US and German army could even fight. But, for a general comparison, the US had a far greater industrial capacity than Germany and would be capable of massing more tanks, planes, etc. Germany had a weaker industrial base but a much stronger officer corps and an army of experienced well trained soldiers that are NOT suffering millions of casualties in the East. The US Army in 1941 was practically worthless - inexperienced, poorly equipped, and quite small, but by 1945 they were incredibly powerful. The German Army in 1941 on the other hand is at the top of its game - fully equipped and experienced, while in 1945 it is a shell of its former self after years of battle against numerically and materially superior foes. In 1945 the Germans are using vast numbers of old men, children, wounded soldiers, and foreigners to fill out their ranks.