If the Kenjutsu guy has no empty-hand training, he's really in no position to with this. "Reflexes and such" are predicated on a greater range and fewer weapons than he's used to. Can you take a golfer and expect him to compete with a soccer player, just because they both move a ball along the ground? It's an analogous situation here.

No weapons, the muay thai would have the advantage but kenjutsu was almost never trained alone so the muay thai guy might not have that large of an advantage

Unless the kenjutsu practitioner objective is to run away while using his "reflexes" to escape, most likely MT will have the overall advantage in empty hand fighting

Most kenjutsu students train in some style of japanese jujutsu, kenjutsu and large circle jujutsu have similar movements as well as complement eachother.

either way the better fighter would prevail

I'd say the muay thai guy wins. Muay thai guy is comfortable in 3 ranges, kenjutsu guy usually only trains in 1 range. Even if the kenjutsu guy had his sword, what if they were fighting in an elevator? etc.

I'll answer your question with another question. Which would you fear more? Someone who have never thrown a punch or someone who throw punches everyday?

m t hands down

Who would win? Obviously skilled man with a sword would succeed. But what about if they were both unarmed. Would the mental teachings of Kenjutsu (reflexes and such) prevail? Also what about the the sword techniques? Perhaps some could be make shifted to work without the sword?