Both 1939 and 1963 versions have been supposedly based on the same book, ''CORAZON'' by Edmundo D'Amicis, and I say supposedly because there is a difference between them. As I have not read the book, don't know who changed what, Alejandro Galindo or Julio Bracho.
1939: The teacher knows his pupils and tries to help them as much as he can. Not only teaches them their lessons but teaches them to become better persons. So much that in the end, after a very important test, some of them are rewarded with scholarships and medals.
1963: The teacher arrives as a substitute after the old teacher dies. He learns about each kid and tries to help them as much as he can. Not only teaches them their lessons but teaches them to become better persons. One of the kids, leaves the town to go to the big city searching for his mother, who works there.
Both movies are very good. But I still think the remake was not necessary.