It's debatable whether they really had a choice. Have you ever listened to Dan Carlin's
series on the Japanese in WW2? It's pretty eye-opening.
I'm not sure 'fair fight' etc. rules are always the problem - we used an absolutely no holds barred strategy against North Korea and we still didn't win that war, despite apparently destroying every single building in the country. We just sent them underground.
Key to winning a war is knowing what you are fighting for to begin with.
I agree a qualitative edge was needed by both the Japanese and the Germans, and they both demonstrated how effective that cold be in an age of rapidly advancing technological development. But neither Germany or Japan prepared for an intermediate phase between (to use in a general and not specific sense) "Blitzkrieg" and full attrition warfare.
With regard to fighters, both had excellent but also seriously flawed designs - the German Bf 109 and later Fw 190, the Japanese A6M and Ki43. The Bf 109 was crippled by a lack of range, the A6M by a lack of armor etc.. Both were excellent, war-winning designs in 1941. By 1943 though both were showing their age a bit. The Bf 109 was still a good interceptor and short range air superiority fighter, but they really needed a longer ranged fighter and they were losing their edge against the competition in general. The Fw 190 fixed that for a while, but it too fell behind the competition (or at least, didn't remain decisively ahead).
The A6M was still a good carrier fighter but they really needed something more robust, higher flying and faster both for use as interceptors and for the attrition campaigns going on in the Islands. Ki-43 while very good, was not ideal for attrition warfare and was fairly useless against high altitude bombers.
Neither country fielded significant new fighters in 1942 or 1943. Only incremental improvements or what amounted to failed projects. The Germans could have had what they needed with the Jets, but for complex reasons that didn't work out. If it had been available earlier, things could have been seriously strained for the Allies.
One problem the Germans had was a lack of certain rare metals and elements needed to make jet engines. Interestingly the Japanese had many of these materials, but had no easy way to get them to Germany. The I-53 submarine, which was sunk by the Americans, contained 9.8 tons of
molybdenum, 11 tons of
tungsten which would have been helpful in the German war-effort. Molybdenum in particular was one of the rare elements needed to mass produce the Jumo 004 engine. If that sub and a bunch like it had been able to make it to Germany on a routine basis perhaps again, things could have been different.
Japanese submarine I-52 (1942) - Wikipedia
I think the other major Strategic errors made by the main Axis powers was being overly aggressive. The surprise attack at Pearl Harbor probably wasn't necessary - a 24 hour warning probably would not have led to a Japanese defeat IMO (though that could be a good debate. The Germans with their mass-murder program and extermination campaigns in the East made it hard to find middle ground to put it mildly. Thus they instigated a very risky policy that ultimately led to doom. If it had been more like the wars of the earlier pre-industrial eras they may well have ended with Japan and / or Germany expanding their power substantially over the long run.