Setting aside the Allied fighters you mention, do you have numbers on Ki-43 vs A6M vs BF109, or to throw in another you didn't mention, FW-190s?
I did mention FW 190, read the sentence after the one you quoted. I think the FW 190 might indeed be a superior bomber killer. The Japanese did test a Bf109E I believe, and did not rate it compared to their own fighters. They could have license-built it if they wanted to. They did like the engine of course, but had trouble with it. It was the basis for the Ki-61 and some other aircraft.
As for rates of shoot-downs by one aircraft type or another, I do not have any statistics handy, but I know the operational history of the A6M vs B-17s and B-24s in New Guinea and Solomons area from the same kind of data I posted above, and the results are similar but I would say the A6Ms did a bit worse. This may be because they were fighting B-17s more often than B-24s, (I think B-17s were a little tougher) and it may be due to the wild weather in the South Pacific which often allowed aircraft to escape - a lot of recon B-17s ended up ducking into storm clouds. B-17s seemed to operate with some degree of relative impunity over the Solomons as recon, (long shot) anti-shipping strikes, and occasional low level raids on ports and airfields. I don't think you could say the losses were hugely different, but I suspect the Army did a little better against the US Heavy bombers- both in the Solomons and in Burma.
As for Bf 109s vs US Heavy bombers, i.e. without a lot of heavy fighters and special weapons, gun packs etc., I don't know about NW Europe 8th AF etc., but I do know the operational history in North Africa fairly well, and I can tell you that B-17s and B-24s did not get slaughtered there, though they were almost always escorted. Loss rates weren't much higher than they were in Burma, I'd guess (just a guess I haven't done a statistical sample).
FW 190s were present in North Africa intermittently, starting in early 1943 I think, (2 JG) and they wrought some havoc against Allied fighters, may have put a dent in the heavy bombers too I need to go back and check, but nothing as dramatic as we later saw in Schweinfurt / Regansburg etc. To really slaughter the US heavies the Germans definitely ramped up their efforts, including the heavy fighters and extra guns etc.
My reading indicates that cannon-armed fighters were more potent against Allied heavies, which is supported though not proven by the fact that Axis fighters increased cannon armament in both caliber, ammo storage, and barrel numbers.
This was clearly the approach the Germans took, I'm just pointing out there appeared to be more than one way to skin that proverbial cat, at least to a point.
If two machine guns were so deadly, why the trouble and expense of uparming/upammoing their fighters to cannons and stowage, as both the Germans and Japanese did?
All things being equal, having more and heavier guns is better. But we do certainly know that many aircraft suffered from the extra weight of heavier guns - notably the Bf 109G series, especially those with the gun pods, were less agile and more vulnerable to Allied fighters, right?
My point here is that aircraft design is to some extent a trade off along the lines of paper / scissors / rock. You want good handling, fast roll rate, turn rate, speed, acceleration, climb, dive, armor, self sealing tanks, heavy guns, more and heavier guns, long range (large fuel capacity and / or great fuel efficiency), altitude performance (high ceiling). You may not be able to have all of these things in the same aircraft.
Which elements were found in a given aircraft depended in part on the Theater.
We know that the early Spitfires (up to the VIII) did not do so well in the Pacific or CBI Theaters. I don't think that the Bf 109, MC 202, Yak 1, or La 5 would have either. FW 190 maybe to a point, but it was also limited by short range.