It is impossible to say which ww2 fighter is the best, as some types never met. Also, NO fighter was excellent at low AND high altitude. Somebody would have to choose the BEST candidate based on the mission and then choose a BEST fighter from each country.
The Germans did have outstanding aircraft all through the war, but to say that they were the best would be wrong. They did get a jet fighter in the air first, but that did not affect the outcome at all. The Me 262 could not be touched at altitude, but when they were taking off and landing they were a sitting duck. The throttles in those things could only be VERY gradually moved back and forth, or a burnout/flameout would happen and he would then have NO power. A non-jet fighter aircraft could just go on the throttle and turn away from an attacker if they were pounced on during takeoff and landings.
The best American fighter at 20,000 feet and lower was easily the Corsair.
It's combination of speed, agility, firepower, range, warload, survivability and adaptability were at a level that no other U.S. plane could touch. The Germans never saw this plane with the exception of a few that flew for the FAA. The Jap aces after the war ALL said that it was the Corsair that they feared the most. Had the early teething problems with the F4U been fixed sooner, there would of have been no need for the F6F. In a fictional dogfight between the F6F and the F4U, all the F6F pilot could do would be to turn defensive circles (Lufberry's) The Hellcat was outmatched in every other category by the Corsair with the possible exception of range but as the Hellcat could only carry 3 theoretical drop tanks versus the 5 theoretical of the Corsair that could then be erased. The Mustang was actually put up against the F4U in carrier trials and mock combat (1943). Three Mustangs had their landing gear strengthened, various other structural upgrades, and givin' a tailhook. It was discovered that at low altitude(10,000 feet and lower) the Corsair was decidedly superior. At medium heights(10,000 - 20,000 feet) the F4U advantage started to fall off some, but the Corsair was still the fighter that you wanted to be in. At high altitude(20,000 feet and higher) the tables turned and the Mustang was the better plane.
Brits
Throughout the entire war the Spit was the best fighter the English had and it was fantastic. Ask any German ace what he thought about the Spit with a skilled pilot at the controls. The Spit was a fine plane and a match for anything up high.
Krauts
Early on the Me-109 was the best thing for the Germans. Against the current model Spitfires, the Me-109 had some advantages, but this could be offset by comparative pilot skill and the location of the fight. The E, F, and G model 109's were superb, lightweight fighter aircraft. The greatest fighter aces of all time ALL flew this plane. Erich Hartman shot down 352 enemy planes with one of these things. That speaks pretty loud.
Later on AND down at lower altitudes with possibly some action at the medium heights, the butcher bird was the hot thing the Germans had. The Fw-190 was made to kill and that is what it did. Many German aces racked up huge scores with these things. A FW-190 with a good pilot and staying within it's flight envelope was a stout opponent.
Japs
The Zero up until 1943 was superior to anything the Americans had. Mitsubishi made most of Japan's single engine fighters and basically all of the later fighters were just building on the Zero. As agile as a falcon and having the range of an albatross the Zero was put up on a pedestal by the Americans. Had the Germans got the diagrams for these planes in 1941, things might of have been different in Europe. Later in the war, the Jack and the Frank were similar and an improvement over the Zero or Zeke. But how good these were are never going to be known. Jacks and Franks found things pretty tough going up against literally swarms of Hellcats, Corsairs, and Lightnings.
Rusky's
Early in the war the Reds were in deep do-do. A series of costly decisions by the German ground machine gave the people of the Soviet Union a breather and the momentum swung against the Germans. The Soviet Fighters early in the war were all lackluster 1930 designs and not wirth mentioning, BUT, later in the war the Mig-3, Yak-3, Yak-7, and some of the Lagg fighters were all excellent, even outstanding fighter aircraft. Sparking one of the greatest turnarounds in history. Some of the Russian types were so feared, that the German pilots were told to avoid them. Another note was that if the German pilot was shot down behind the Russian lines, his future was definately not going to be fun. After the war, some of the Russian types were made available to the Americans and they were absolutely amazed at their performance.