Jesus had a very specific message he wanted to bring to the world. It’s a very similar message as those given by the other great prophets of Jewish literature. God is the source of all things good in the world. Choose to obey the spirit of God’s commands rather than the literal meaning of the recorded words. Belief is power, belief in God is ultimate power. Love is the ultimate meaning behind creation.
The Buddha’s message was, roughly, that liberation from hell could be obtained through meditation and insight. Just like Jesus, the Buddha set his path apart from established spiritual wisdom. Jesus fought against law, arrogance, and hard-heartedness, the Buddha fought against the massive ecosystem of supposedly spiritual truths that never seemed to get anybody anywhere.
If you put them in a room together, and gave each the advantage of understanding the social milieu that the other emerged from, and insight into the underlying message of each other’s teachings, I don’t think they would find many points of contention to disagree on. Both were practically concerned with people’s intentions and their actions.
Jesus’s words that later got turned into the Christian doctrine of ‘faith, not works’, is remarkably similar in essence to the Buddha’s dictum that you should seek the truth out for yourself rather than just believe what others tell you. They both place the source for truth internally.
It may seem strange to think that faith in God means you’re getting your truth from within, but when you think about precisely where you need to turn in order to get your input from God, it becomes much clearer. Jesus took great care to pray with anybody who needed or wanted it.
Less is known about the Buddha’s specific approach to pedagogy, but his practicality and distaste for codifying his teachings into writings would indicate that he, too, would take the time to meditate with anyone who wanted to learn.
It’s commonly believed that the Buddha was an atheist. If this is true, and bear in mind that we have no real reason to saddle the Buddha with such a thing, then he could have maybe had a quarrel with Jesus over the Jewish God and whether theirs really was the best.
But it’s unlikely in the extreme that the Buddha would actually choose to debate someone over this, gleaning over the available historical sources indicates that the Buddha simply wasn’t interested in such questions. Jesus would have recognized that the Buddha wasn’t a Jew and so he wouldn’t have beaten Gautama over the head for forsaking a deity that he could have never known in the first place.
If Jesus saw fit to make that point, he might have just performed a miracle, though this would have gone against why Jesus did miracles. Jesus performed miracles when 1) there was something that needed to be done and 2) God wanted to send the message, Performing a miracle just to make a point would have violated both conditions.
No, Jesus and Buddha both wanted to point out hypocrisy, and neither would have been able to find it in the other’s words or deeds. Neither were dogmatic. I can only imagine them having had a fruitful, productive discussion on the finer points of their respective experiences, Jesus as possessing the revealed understanding and power of the divine, and Buddha of piercing insight into the self.
At the end of the day, they would have both come to the conclusion that they’re two sides of the same coin.