In studying the histories of the D-Day invasion, we would have to give the edge of superior weapons to the Germans. In tanks, machine guns, artillery they had a decisive edge.
Thank God we had air superiority, but the errors committed on that day, almost doomed the invasion. It was the courage, tenacity, and resourcefulness of the American soldier which saved the day. The sacrifices made on June 6th 1944 will forever give glory to the annals freedom. May God continue to bless the legacy of those men.
Fortunately for us, Der Fuehrer was an idiot, who remained convinced the main assault was still going to be at Calais, even after the invasion began.
The U.S. had overwhelming numerical superiority in artillery in Europe, something like 7:1. In addition U.S. artillery was superior in quality and American artillery tactics were superior. Compounding the American advantage was a shortage of ammunition for the Germans, and compromise in lethality caused by shortage of chemical feedstocks for explosives. German shells were often filled with as much as 50% salt because of lack of explosives.
The most formidible German armor was superior to most U.S. armor, but clearly the advantage was not decisive. For the most part German armor was comparable or inferior to the Sherman. Tigers and Royal Tigers were the exception, not the rule. The U.S. enjoyed 5:1 numerical superiority in armor and probably a slight qualitative edge. U.S. armor was also more mantainable, with close to 100% availability, while German armor had a mean distance to repair of about 100 km. German logistics and repair were also distinctly substandard, meaning a disabled tank that might have been recovered and repaired by Americans, was generally a causuality for the Germans. In some ways, the largest German tanks were not particularly practical. The Royal Tiger at 70 tons could not traverse many common road bridges, consumed more fuel than the Germans could supply, and attracted a lot of direct fire artillery and P-47 Thunderbolt attacks. It was more of a semi-mobile pillbox than a tank.
German infantry weapons were probably superior to U.S., admittedly, but the big issues were airpower and artillery, with armor a close second. Infantry weapons are a distant third as a determinant of the outcome of victory.