Presumably this man converted to Buddhism because he became convinced that what Buddhism teaches is correct, and that alternative viewpoints are mistaken. This action would seem to indicate that in his own understanding, Buddhism and Christianity are not the same: if they were, what need would there be to convert from one to the other?

Any direct comparison of their teachings will demonstrate that they are not the same. As one obvious example, Buddhism teaches that people live many lifetimes, reincarnating after they die, before they become sufficiently enlightened to become at one with the nothingness, thus escaping the dreary cycle of rebirth. Meanwhile, Christianity proposes that people live one life, and then die and, because of the grace of Jesus on the cross, enter into the presence of the Lord. These teachings are clearly different.

In terms of your conversation with this man, you might clarify whether he thinks the two religions teach the same thing about salvation.

If he says they do not, you could ask if he thinks that Christians should have the right to tell Buddhists what they must believe and say about salvation. After he says No, you can turn it around and ask if Buddhists should have the right to tell Christians what to believe and say. Perhaps you can suggest that his anger might not help him reach enlightenment; and that if he has found peace in choosing a different path from the way of Jesus, it need not offend him when a Christian seeks to understand and follow Jesus. A fruitful conversation might emerge if you ask, “Since Buddhists and Christians think quite differently about salvation, how can they discuss these matter together in helpful ways?”

If instead he says the two religions do teach all the same things, then so far he is only dabbling in Buddhism. You might enjoy quite an interesting conversation if you were to ask him, “What is it about Buddhism that has attracted your interest?” You could then respond with some reflection on how believing in Jesus has made a difference in your Christian walk.