The match-up between Mike Barnes and Daniel LaRusso
It has often been claimed that it's quite surprising how Daniel LaRusso was able to prevail over Chozen and was generally competitive against him whenever they faced each other in Japan, but had an extremely hard time handling Mike Barnes. While I agree that at a first glance it doesn't make sense how Daniel is so convincingly defeated by Mike during their first two encounters, I actually did find this aspect of the story to be realistic.
I play racquet sports such as tennis and table tennis (which do have certain similarities to karate when it comes to the need to display great reflexes, hand-eye coordination, and quick thinking). I have personally experienced how you can win relatively easily against a certain player and the same opponent who has a losing record against you is able to gain the upper hand over another competitor who you stand almost no chance against. It's simply a matter of how different playing styles match against each other, unless of course the gulf when it comes to one's grasp of the fundamentals of the sport is way too wide.
Even if Barnes had retained his perfect record against LaRusso, it's not out of the question that he could have suffered a defeat against Chozen.
Of course Barnes' confidence in his own abilities and him being able to successfully intimidate LaRusso from the very beginning also set the course.