I have a few things to add
As someone who has studied WWII and it's weapons for the last 40 years, I would like to add a few things to the discussion.
First of all, there are two different ways of measuring "better", by design, and by success in use. There were a number of German designs which were superior to those in use by the Allies, but were not produced in sufficient numbers to have a significant effect on the war effort. The most famous of these are the jet fighters, the Sturmgewehr, and the last model U-boats.
Infantry weapons; Yes, the M1 Garand clearly proved itself to be the premier infantry rifle of WWII. However, Garands were not as widely used as some here tend to think. Many US Army units fought the entire war carrying M1903 Springfields, and our Marines fought all of the early island campaign with the 1903 as their primary rifle. It wasn't until about the middle of the war that the Garand became the primary combat rifle in terms of numbers.
Many have made mention of the fact that the Germans did not have a heavy machinegun to match our M2 .50cal. True, however, it was only due to their doctrine, not their engineering/manufacturing potential. The MG 34 and later the MG 42 were dual purpose machineguns. Tripod mounted the filled the heavy machinegun role. And the Germans fielded large numbers of 20mm cannon, which went along way to matching the ground role for a heavy MG.
The German Navy never had a chance. Because of Hitler. When Hitler took power he assured his armed forces that there would be no war before 1945. Kriegsmarine construction was based on that assurance. When Hitler launched the war in Sept 1939, the Kriegsmarine was caught far behind, and never caught up. For example, it was determined that 300 U-boats were needed to close the Atlantic. They went to war with about 100, and nearly got the job done anyway. But they paid a heavy price, during the war 40,000 young Germans went to sea in U-boats. 30,000 never came home. The surface fleet would have been small, but well balanced and powerful in 1945 as well, with modern battleships and aricraft carriers. It likely would not have made a difference in the long run, but they never got the chance to find out. As others have noted, they never got the bugs out of their powerplant designs, and the small numbers of capital ships and the way they were used allowed the Royal Navy to overwhelm them.
As far as German soldiers being unable to act without orders, those of you who think this need to do more research, in particular the accounts of men who were there. More than one veteran US officer was of the opinion that the most dangerous opponent to face was a German soldier without orders. German soldiers at lower levels were trained to adapt and improvise in the absence of orders, and the Wehrmacht relied heavily in "saddle orders", which basically is "take the objective", relying on the initative of junior officers to get the job done. It worked rather well on the tactical level.
There are lots of places where the Germans made what turned out to be very serious mistakes, but the most serious one was Adolph Hitler. His leadership got them to start the war before their military was ready, and later his micromanaging cost them dearly. Another "mistake" was one that the Japanese fell victim to as well, at first, they were successfull. In fact they succeeded beyond their wildest dreams. For a while. They then fell victim to "Victory Disease".
Both Germany and Japan retarded or abandoned future weapons design and developement for a time, because they were "not needed". Until reverses on the combat fronts proved them wrong. The time lag to design and bring superior weapons into service was never made up. There are many examples of this, notably in aircraft. By the time superior designs were built, combat pressure did not allow them to be built in sufficient quantity to be effective. Limited industrial capability, compared to the USA and the Soviet Union also played a large role. Both germany and Japan could not afford to interrupt the production of the Me 109 and the Zero to switch over to better fighters, even though those two designs had reached their peak potential by 1943. The US, on the other hand, with vase resources, and the luxury of time was able to gear up to production levels that allowed sufficient supplies for combat and produce improved designs, and integrate them into the combat forces.
Roosevelt turning this nation into the "Arsenel of Democracy" years before we actually went into combat went a long way to laying the goundwork for our success.
Both Germany and Japan based their plans on a short war, and when the Allies refused to make peace after being beaten, it screwed up their plans. They had not planned for, nor equipped for a long war. They had no long range heavy bombers, for example. The Germans had no long range single engine fighters, by their doctrine, they didn't need them. Neither did the British for that matter. The Japanese did, but only because they planned from the beginning to fight over long ocean distances.
By the way, the Sturmgewehr (MP 43, 44, and Stg 44) were forbidden to be made by Hitler. His armies didn't
need another rifle, which is why they were originally called MPs (Maschinen Pistole -machine pistols-submachine guns). It was only because of some Wehrmacht officers working around Hitler's orders that they got any into the hands of the troops. After they were in use on the Eastern Front (in small numbers) and proved sucessful did Hitler relent and authorize production. Again, too little, too late.
Hitler did something similar with the jet fighter. After seeing the prototypes (which could have been fielded a year earlier but for Victory Disease), he ordered them to be converted to bombers, which delayed their operational use by another half a year.
The war is full of blunders like that, many on our side as well. Our policy of having tanks support infantry and having tank destroyers fight enemy tanks turned out to be seriously flawed. But in the end it can be summed up in one of my favorite old jokes;
German officer (being questioned):
"Ve haff ze best tanks in ze vorlt! One uf our tanks iz wurth ten uf your tanks!
Cocky GI:
"oh yeah? Then how come we're kicking your ass?!
German Officer:
"Because you alvays haff elefen!
