Which character matures the most throughout The Prince and the Pauper? What are examples of that change?

I would have to say that Edward, Prince of Wales, matures the most throughout the novel.
Edward had good manners throughout the book due to his training as a prince. He deepens and matures through his experiences. These start the moment he meets Tom. Edward responds sympathetically to Tom’s account of his life, and when he hears Tom gets beaten, tells him “BEATINGS!—and thou so frail and little. Hark ye: before the night come, she shall hie her to the Tower. The King my father"—
Tom interrupts, saying, "In sooth, you forget, sir, her low degree. The Tower is for the great alone."
Edward has a better formal education, but Tom understands the way of the world and that there are major differences in how the rich and noble experience the world compared to how the poor experience it.
Edward's experiences once he seems to be poor fundamentally change him for the better. Twain summarizes these changes in the novel’s conclusion. Edward acts more ethically toward individuals and works to make things better for his people as a whole. He matures by moving from sympathy to active ethical action.