You will probably get some differing viewpoints on this from many teachers, but I believe Jim learns more.
First of all, Jim is the narrator, so we are privy to his innermost thoughts. The story of Antonia is only told through Jim's narrative, and Jim's perspective, so we truly don't know what she learns, just what Jim thinks she may have learned.
Also, from the beginning, Jim is a brooding, alienated (orphaned), cerbral character. He learns a lot about who he is and who he is not from observing the way Antonia lives, the way she interacts with her family and others (not always to her betterman), and by weighing his own philosophies and way of life against hers, he learns more about himself. We don't have any evidence in the novel that Antonia does this in return. In fact, she mostly rejects the way Jim chooses to do things and when he gives her advice about some of the mistakes he thinks she is making, she ignores it.
Finally, at the end of the novel, it is Jim who returns to Nebraska seeking out some solace after his failed marriage. He is a successful attorney, but his life is empty and lonely. He admires what Antonia has, a loving husband, a big family, and he again compares his life to hers and finds his lacking.
Jim is Willa Cather's "voice" as well as a character, therefore his lessons, I believe, are the more prominent ones.