Thomas Kuhn's book The Structure of Scientific Revolutions managed to shake one of the fundamental ideas of the current era. Science is seen as a monolithic body of knowledge giving us absolute certainty about the physical world. Kuhn, a historian of science first and foremost, pointed out that science continually changes in its methodology based on differing fundamental assumptions. He used the phrase incommensurable to describe different eras of science he labeled paradigms. Medieval science was one paradigm, Newtonian science is another, and Einsteinian science is the most recent.
The idea that that they are incommensurable is that they can't be compared with each other because they operate by these different assumptions, and in order to compare them, you need one objective set of assumptions, which will inevitably favor one over the other. Medieval science may not be as technologically advanced as ours, but we don't have a place for gods in our materialistic science, which would've been an anathema a millennium ago. Of course Medieval science looks backwards to us - we're judging it by the standards we've internalized over the past four centuries. It doesn't play by the rules we like.
I'm not trying to start a flame war over religion or science here, so if you're further interested in Kuhn, I recommend reading this article, while I bring my idea back to relevancy. Consider boxing and MMA to be different paradigms of the same body of work. They are both combat sports (like Aristotle and Newton are both scientists), but the rules (i.e. assumptions) both sports use create a gulf of incompatibility.
There has been talk of how Floyd Mayweather and Manny Pacquiao would lose in MMA despite being the best boxers in the world, KJ Noons wanting to welcome Pacquiao to MMA, Herschel Walker defending our fine sport from boxing, and so on. The rivalry between MMA and boxing (while perhaps overblown) can be intense, but if analyzed with Kuhn's ideas, it's also meaningless.
Let's say that Floyd Mayweather and Uriah Faber decided to fight. Who would win? It depends on what rules would they use. In a boxing match, obviously Mayweather would win - he's one of the greatest strikers in the world. In MMA, Faber would easily take him down and at a minimum grind out a lopsided decision (would Money tap out to the mount?). So who's the better fighter? Faber has a more well-rounded skill set, but Mayweather has developed one particular skill to its limit (a question of breadth vs. depth).
Even saying that MMA is more realistic than boxing doesn't work well because it's real compared to what? If you're referring to a street fight, the winner is the guy with a gun. If it's self defense, then BJJ isn't necessarily good because you leave yourself vulnerable to attack from another person while on the ground. To real warfare? That's ignoring weapons and group tactics.
While I'm singling out boxing, this same discussion can apply to any lone martial art when compared to MMA. Ben Askren says he'd destroy Georges St-Pierre in a wrestling match, and he's probably right . GSP picked wrestling up after starting MMA, while Askren has practiced it for nearly his whole life. However, GSP has adapted it to MMA far better than anyone before him, combining strikes with takedowns to constantly keep his opponents guessing and preventing them from getting comfortable (though another life-long wrestler, Josh Koscheck, is looking to halt that trend). Askren would lose decisively to GSP right now in the octagon.
I would argue that we're in a combat sports paradigm shift of sorts. Kuhn argues that as a new scientific idea emerges, it may take the old establishment to fade away before it becomes accepted. Boxing has been the preeminent combat sport, but it is largely in decline. MMA is still increasing in popularity, and more and more kids are training. High school and college wrestlers are seeing it as a viable career, and youth are beginning to train MMA as a whole rather than any one aspect, giving future athletes in our fine sports a well-roundedness unheard of nowadays. As time progresses, the "old guard" of boxing fans will give way to the younger, hungrier combat sports fans, just as the Aristotelians gave way to the Newtonians. The history of MMA is the collision of martial arts from around the world under a new combat sport paradigm. Nearly every technique is considered legal (thought that isn't enough for most fans) in an attempt to give every style a fair chance. The idea of being a one-dimensional fighter in MMA is often derided. As MMA expands into more markets like the Middle East and China, we'll see an influx of even more exotic styles, further rendering the old paradigm (seemingly) obsolete. Much is unknown about how MMA will continue to evolve as the new standard-bearer for fighting, but it promises to be interesting.