An impressive runoff, it's amazing America has won so many wars. What nation do you think has a better record of military procurement, logistics, and strategic planning? By the way I must admit I can't spell to save my life, but I think it's spelled America, and Americans.
Breaking it down by category.... WWII era
Military procurement depends on what roles/missions/methods time periods is, so that general question is extremely case sensitive.
WW II tanks, artillery (includes control systems for ground, naval and AAA) and motorized systems.
Hard to beat the Stuart/Sherman/Jackson combo. American trucks were golden. Artillery; tubes and rockets with control systems... American, Just the equipment... RUSSIANs.
Small arms as a class set.
The Czechs, but they are functionally removed as they are 1938ed. Next best? Probably the British, but they take mid-war to get there. I think American gear is good enough like Russian gear, but it could have been better if 1933-1935 programs (Ruger machine gun, an improved Brandt mortar, and a more refined Garand) had been available. One sore spot is grenades. US ones are NTG.
Warships.
Americans without a doubt class for class and method for method are the Wally standard. The Japanese are so close I would consider it a coin flip.
Aircraft technical>
Across the line, the coin toss is British or American. The Russians fielded some goodn gear but it was not watts supported or as efficient in burden and in flight characteristics as the Wally gear. Special case: bombers... British for the aircraft and the conventional bombs and aiming systems for TAC-AIR and strategic bombing.
Aircraft use>
Despite the smattering of one offs and specialist missions for which the RAF is justifiably famous, they were LOUSY at the air campaign. USAAF, despite its numerous faults, was the best of the air forces in WWII in this regard late with the Japanese being the best early. This is not even debatable. They, both, had their priorities right when they finally got it together (USAAF in 1944). Kill the enemy air force (as in the trained aircrews in battle.) first and then go after the enemy infrastructure at the bottlenecks. The RAF tried to avoid this problem in Europe by night bombing. Kannhuber nixed that, then the USAAF 8th nixed his night-fighter force along with the day-fighters in Feb, 1944..
In the Pacific; it was the 5th USAAF, New Zealanders and especially the Australians who got it done.
Strategic planning and logistics (The two are inseparable.) in this case set is RAINBOW 5. It was the actual allied plan that won the war. The British before it, did not even have one. The Russians were ad-hocked up to their bleeding eyeballs. Once everyone Wally and co-belligerent (Russians), got on the same planning set and tailored their inputs and ops to it, that meant the Axis were doomed. It is not strictly an American Plan by any sense as the myths have it, but an Anglo-American one with a LOT of US Army industrial planning input into the op-art nuts and bolts and a lot of British objectives that dovetailed with American (USN ABC staff talks in 1941.) naval planning for Black and Orange.