Did we though? I guess we did remove all of Luftwaffe and Imperial Air Service from the air. Never seen any numbers for fighters vs fighters fights. Germany was certainly pushing the tech by the end of the war.
The tech didn't help them because of the absolutely massive amount of large, durable, well-armed planes we built both before and during our time in the war. We really let the British struggle for a good while before stepping in and dominating the air relatively quickly, with the good ol' American way: blunt fuckin' force.
From
Wikipedia:
Air losses:
Germany: Estimated total number of destroyed and damaged for the war totaled 116,875 aircraft, of which 70,000 were total losses and the remainder significantly damaged. By type, losses totaled 41,452 fighters, 22,037 bombers, 15,428 trainers, 10,221 twin-engine fighters, 5,548 ground attack, 6,733 reconnaissance, and 6,141 transports.
Japan: Estimates vary from 35,000 to 50,000 total losses, with about 20,000 lost operationally.
Soviet Union: Total losses were over 106,400 including 88,300 combat types.
United States: Total losses were nearly 45,000, including 22,951 operational losses (18,418 in Europe and 4,533 in the Pacific).
So our 'operational losses' (planes where the pilot was killed or bailed, I'm assuming here) in total were only about as much as Japan's, who dominated the Pacific with a relatively meager force, mostly through lack of opposition. After Pearl Harbor, eh...I'll never comprehend why they thought an aerial attack on a US base was a good idea. I'm sure it was already well-known that we were pretty hard at work both building our forces and supplying our allies.
Some other war buff can probably give an accurate account, but AFAIK we gained air superiority over Japan inside of a year. I dunno, maybe it took until 1943.
And the Luftwaffe was pretty mortally wounded following D-Day. I don't think we had much of an air operation in Europe (aside from Italy) until then.