This question isn't really worth posing. To be fair to both you'd have to alter the rules of each sports to try to make a fight between athletes of different sports. So the result wouldn't mean much really.
If you take a MMA guy and make him box against a boxer he'll get most likely destroyed as you take away many key element of MMA. If you take a boxer and make him fight an MMA fight he'll most likely get destroyed as he's not used to kicking and fighting on the floor...
I agree, however that isn't really the issue behind this all. It's obvious a wrestler is the best at wresting, boxing at boxing an so on.
But the issue is in regards to who are the best fighters in the world, period - not just at their own sport. Boxers fight in boxing, like wrestlers in wrestling, muay thai, Jiu-Jitsu etc...so why isn’t it fair for a boxer to fight in MMA? MMA isn’t just one sport, it’s a combination of many sports with a a more unified set of rules to justify this. An endless amount of people from different disciplines have made the transition, the only difference is that those others fighters have adapted to fight.
A boxer simply isn't the best fighter in the world, as many boxers claim themselves and the sport to be. Boxing is only one aspect of fighting. MMA is more credible in that claim because a MMA fight accepts many disciplines and shows a better overall judgement. And for example boxer will generally lose to a kickboxer because boxers don't train for kicks and can hardly take them, if any evidence just watch K1 fights where boxers entered (Ray Mercer certainly didn't last long in his couple K1 fights). Boxers are also defenseless on even many basic ground skills so what happens if a boxer get's taken down? A boxer is only effective on stand-up, and in a MMA his jabbing is far less effective.
So anyways, the point is, if you were to take every top fighter in the world and let them fight, being a well-rounded MMA fighter would be of the best strategy, as opposed to being a one-dimensional fighter be it boxer, kickboxer, wrestler etc. In MMA you don't see too many top level fighters who are well-versed in only one discipline and for those very reasons. There isn't one style of fighting that is the best, but to be the best fighter in the world you'd have to beat the best fighters regardless of how they fight.
