Prince Hal is divided and complicated. He is the son of the king, but spends much time away from court. He spends time with common men, and, in Falstaff and his friends, with men of no honor. He is thoughtful where Hotspur is brash, and, as a result of his explorations, understands the complex nature of his society better.
By contrast, Henry Percy is "the king of honor." He is bold, poetic, daring. His spirit is fierce and runs hot. He's ready to challenge the world—in fact, he almost literally challenges the world, so long as he can gain honor, as you can see here:
By heavens, methinks it were an easy leap,
To pluck bright honor from the pale-fac'd moon,
Or dive into the bottom of the deep,
Where fathom-line could never touch the ground,
And pluck up drowned honor by the locks.