Muay Thai vs BJJ [Brazilian Jiu-Jitsu]: what would be the outcome of this fight? Brazilian Jiu Jitsu is a grappling style while Muay Thai is stand-up striking style. Both systems are used in MMA and they complement each other rather than compete. In the early days of the UFC BJJ was very dominant thanks to Royce Gracie and his grappling skills. Since then most of the fighters started to train both: stand up striking and grappling/wrestling techniques to be more versatile.
Brazilian jiu-jitsu is focused on ground fighting and grappling and it doesn't involve any stand-up striking techniques. Muay Thai, on the other hand, focuses on kick and punches and occassionaly getting into clinch but it doesn't allow any ground game. Like I said before, those two styles compliment each other more than anything else and are not meant to compete with each other.
It's like comparing a sniper rifle and a shotgun: both are lethal weapons in their own way but build for a different purpose and with a different range of effective damage inbuild. Jules from Pulp Fiction would say: It's not the same ballpark, it ain't the same league, it's not even the same game.
Let assume that two guys with different fighting backgrounds, one in Muaythai and another one in Brazilian Jiu Jitsu, wanted to fight each other. What would happen next? Thai fighter would most likely keep him on distance smashing his face with devastating kicks and punches. BJJ fighter wouldn't have any stand up skills to compete with Muay Thai strikes. And that would be it. End of the fight - KO or TKO in the best case scenario.
OK, lets assume that a BJJ adept grabbed a Muaythai fighter, thrown him on the ground and trapped him with a spinal lock or an armbar. In this case, Muay Thai fighter would be helpless not having any effective skills to fight in this position and to counter a submission attempt. Most likely he would get choked and passed out. This could happen on the street and bit less likely in the ring with an experienced fighter skilled in using a reach advantage for the purpose of winning the fight.
So I guess it all boils down to the level of Muay Thai guy takedown defense since he would have a tremendous advantage fighting in a stand-up. Another factor would be how fast the BJJ guy is at taking someone down in spite of a kicks and punches he would receive in the process.
Muay Thai is very effective in a stand-up and BJJ is very effective on the ground. In my opinion, both styles work great when combined - just like Western boxing and wrestling powerful combination. When you combine skills to fight on distance with the ability to effectively fight on the ground you can build a more comprehensive strategy. This way you will not get surprised easily by your opponent inside or outside of the ring. This approach makes complete fighter, capable of handling a difficult situation and dealing with any outcome of the fight.
Check out this interesting Muay Thai v BJJ match online: