I'm going to be a little nerdy here and use some rather clear-cut and obvious examples of a villain vs an antagonist, using enemies of Batman....
Yes, I know ... Batman? Really? Yes, really. Why? Because everyone at least knows of the majority of the Batman rogue's gallery, so it acts as a good common denominator for everyone involved.
Let's look at some of these folks ...
Few people would think of the Joker as anything less than a villain. And that would be correct -- but what makes him so? A complete and utter disregard for human life, for one. He thinks he's funny when he kills large groups of people, and not only that, but he insists that everyone else finds it funny too.
Is Joker insane? Perhaps -- his fashion sense would indicate that if nothing else -- but does that make him not-evil? It reminds me of the argument that some victims of child abuse go on to become abusers themselves -- which is garbage. I know more victims of child abuse than is possibly good for me, and while they have an array of neuroses and psychoses, none of them have gone on to be abusers themselves.
Even Alan Moore's The Killing Joke insists that Joker is the result of, as he put it, "one very bad day." But, even during that comic, Joker is undermined by his victims. Despite creating a very bad day for police Commissioner Jim Gordon, Gordon stays completely sane, and doesn't go off on a killing spree. He doesn't even put two into Joker's head, which would have been at least justifiable under the heading of "We shoot rabid dogs, don't we?"
The legal definition of insanity is the inability to know the difference between right and wrong. With the Joker, the number of times he theorizes on what he should do next illustrates he's fully well-aware of the difference, he just finds "wrong" a more entertaining option. On the sociopath /sadist scale, he gets a ten.
He might be clinically "insane," but he is also evil. Let's call this a villain. He's not merely the opposition, not put there by circumstances -- he's like this because he wants to be.
In short, when Riddler has been on the wrong side of the law, he has chosen to be this way. And his choice makes him a bad guy. Wikipedia has actually described him as being a malignant narcissist ... which we used to call evil. He's evil and he's having fun. Villain.
In short, "Proving that I'm a super genius is more important than anyone's life," means you're an evil little bastard.
You can see where I'm going with this. At the end of the day, villains are simply evil. But what's an antagonist?
For instance: during the No Man's Land storyline, Two-Face kidnaps police commissioner Gordon and puts him "on trial" for breaking a deal. However, Gordon is saved by a vigorous defense by .... Harvey Dent.
I think this puts him on the straight crazy bent (yes, pun). There's good in him, it's just kinda lost in the white noise that's his brain. Antagonist.
And now for something a little different.
Catwoman is a thief. But she's also been our thief. She robs from the rich, gives to herself, and does the occasional side job for the US government and the CIA. Her later development has put her as more of an anti-hero than even an antagonist.
Though she still occasionally seems to play cat and die Fledermaus, there's still more than enough good in her to proclaim her an antagonist -- when, as, and if she isn't off saving complete strangers because they happen to be within her line of sight when they're in trouble.
And then there's Ivy.
|Cosplay Deviants, DragonCon, 2012|
However, there's a bit of a problem with that. Why, you ask? Because Poison Ivy has had moments where she's protected human beings, despite that she generally thinks humans are inferior to plants. The No Man's Land storyline had her protecting orphaned children in central park and feeding members of the city. She has the occasional breakdown, but she's trying to be a good person. Which is more than I can say for some people I've known in real life.
And, besides, if you turn into vegetable matter and plants talk to you, you'd be a little screwed up in the head as well.
I guess I could go into Harley Quinn, or the Penguin, but I think we'd be beating a dead horse at this point. Harley is now an anti-hero after years of being a poster girl for battered woman syndrome as Joker's girlfriend. The Penguin has retired to being a white collar criminal who runs his own lounge. Bane can't be classified, because his character radically changes depending on who's writing him.
At the end of the day, I never subscribed to the cliche that villains never look in the mirror and see a villain. Or that "they think they're right." Villains don't care about right or wrong. They just care about themselves. An antagonist might be talked down, or persuaded, or brought away from the dark side; there is the possibility of redemption. The villain likes the dark side, has chosen it, and never wants to leave. It's the difference between Hannibal Lecter (of the books) and Sauron. It's the difference between Joker and Two-Face. It's the difference between Heaven and Hell.
At the end of the day, it's why I prefer villains in my novels. When I have an antagonist, I tend to redeem them.... eventually.
And trust me, in A Pius Man, there's an opportunity or two for redemption for some. And others just want to die screaming.