Most armaments experts tend to agree a good example of a 20mm outlay is the best overall choice for ballistics, effective range and effect.
Other weapons were chosen for various reasons. Browning .303 early in the war for Britain due to its proven reliability and the untested nature of either the heavy Browning or Hispano types at the time as far as the Ministry was concerned.
For the US six fifties were found to be more than adequate for virtually all fighter roles, whilst eight fifties an excellent interceptor and ground attack armament. Postwar however they did switch to the 20mm, perhaps this was due to the lack of reliable guns with good ballistics and low weight in the 20mm class in local production any earlier. Even when GB adopted the Hispano for the Spitfire they kept either four .303 and later two .50 Brownings perhaps for fire rate and general reliability, though certainly some a/c like the Typhoon/Tempest had only four Hispano.
During the war probably the best 20mm design was the upsized Beresin used by the Soviets, which was effectively a rechambered .50 cal machine gun. The adaption had almost no effect on gun weight, so generally three were placed in the nose of Soviet fighters making for an accurate and deadly package with a high projectile rate. It fired the same round and had the same ballistics as the highly successful ShVAK.
The MG-151 was good in the early war, being uber-reliable with a good fire rate but was pase by latewar, if at least the standard. Both the ShVAK and MG-151/20 are fairly comparable to a late war Hispano.
The real revolution came with British and French copies of the revolver cannon being developed by Germany. These became the DEFA and Aden, and were originally designed in both 20mm and 30mm variations.
The Browning fifty certainly did suit US fighter training doctrine well. One point rarely considered is that different nations trained their pilots differently, well obviously due to different aircraft types in general use.
American pilots I'd give as having an emphasis of "laying down fire on the target" where Luftwaffe pilots were taught aerial marksmanship (the easiest form of which letting the target fill your windscreen before firing), for obvious reasons. Often they used centrally mounted single cannon.
Even the Lightning originally mounted the Oldsmobile cannon and a couple of defensive thirties, but this was switched almost immediately to a set of fifties with a Hispano for extra punch, maintaining that US fighter training doctrine I think. But even so some P-38 pilots have said they liked the way firing at a target was a different thing than in another fighter type, you shot differently and some preferred the difference. But I think the other way was quicker to teach rookies, faster proficiency with lower expertise perhaps.
So I'd say in conclusion: centrally mounted cannon or wing mounted heavies was either/or very good.