Mugen should win because Finn's only good at fighting big monsters, and even then he's sloppy and lucky and relies on his magic dog to bail him out a lot. Finn's got some kind of superhuman stats, but so does Mugen.
@UltimateHero0406: Is Finn allowed to use ice ninja techniques?
@Mr_Ingenuity: He once tore down a tree that was 4-5 times his size with his bare hands and hit a giant spider with it.
It's really hard to gauge who has better agility since Finn actually does a lot of acrobatics in the middle of and in between fights. Adventure Time just isn't as flashy a show when it comes to showing off skill. One specific showing of Finn's reflexes off the top of my head is catching (not deflecting) an ice arrow that was shot at him by Jake.