He is a hero.
The whole play is a "morality" play, with a virtue/vice comparison between <PERSON> and <PERSON>. But the twist is, from the outset, that <PERSON> is really the virtue (wise, biblical, popular), while <PERSON> is lost in vanity (harebrained, hot blooded) - but brave and honourable, like a legendary giant, with a devout, idealistic maiden in tow:
Prince <PERSON>: ...I am not yet of <PERSON>'s mind, the <PERSON> of the north, he that kills me some six or seven dozen of Scots at a breakfast, washes his hands, and says to his wife “<PERSON> upon this quiet life! I want work.” “O my sweet <PERSON>,” says she, “how many hast thou killed today?” “Give my roan horse a drench,” says he, and answers “Some fourteen,” an hour after. “A trifle, a trifle.". Act 2, Scene 4.
<PERSON> is chivalry, and is considered on the whole to be living up to the expectation of his time. But, ultimately, in vain:
<PERSON>: ...There's honour for you! Here's no vanity! Act 5, Scene 3.
and slightly earlier
<PERSON>: What is honour? A word...Honour is a mere scutcheon - and so ends my catechism. Act 5, Scene 1.
He is definitely not a villain. Perhaps there is similarity to <PERSON>, who is lost in vain. Also, for his hot-bloodedness, I can see similarities with <PERSON> in The Godfather:
<PERSON>: I hope you're not a hot head like your brother <PERSON>, you can't talk business with him. 381
The Godfather.
Is <PERSON> a villain in the Godfather? No way.
Perhaps <PERSON>'s actions are not on the whole "recommended" by <PERSON>, in some sense, but he is given the role of a hero, not a villain. It is more likely <PERSON> is the villain. Consider Henry IV Part 2, where <PERSON> is ultimately cast out, and Henry V, where <PERSON> is hanged. But then, he is too likeable. So there is a deep character comparison going on. If there is a villain, what is being driven out is <PERSON>'s un-kingly life. He is fulfilling his potential. So personalities are so bright and vivacious in the play, it is the opposite (dullness) which is being driven out "with a dagger of lath", leaving the fulfilment of <PERSON> as <PERSON> (again, like in the Godfather). 190