Polite Villains, Rude Heroes

Nicodemus: What would you say if I told you that you and I might have a great many common interests in the future?

Harry: I wouldn't say much of anything. I would be too busy laughing in your face.

—Small Favour, The Dresden Files

Sometimes Good Is Not Nice, hence a hero can be obnoxious and rude. Similarly, sometimes an Affably Evil villain could be friendly or polite. When either or both of these work their way into to the tone of a conversation between a hero and a villain, you end up with conversations in which the villains sound more respectful than the heroes.

Depending on how this is treated in the context of a story, it could serve as a Pet the Dog moment, or alternatively, it could serve as a sign that the villains really, REALLY don't deserve respect and hence the heroes will not give it to them. Then again, that would by its very nature imply the villains at least humble enough to be polite to the heroes... or at least not too proud to pretend to be.

Examples of Polite Villains, Rude Heroes include:

Anime and Manga

Inu-Yasha and his half-brother have no love lost between them. Sesshomaru is formal but contemptuous while Inuyasha is generally rude to almost everyone to begin with. Though Sesshomaru also does insult Inuyashu over being a Hanyo/Half-Demon, so it's kinda hard to think of him as polite when he does that.
Gun X Sword seems to fit. Although Wendy and Joshua are nice enough, Van and Ray and to a lesser extent Carmen 99 are pretty jerkish, while the Claw and all of his minions are a really nice bunch.
Panty & Stocking with Garterbelt zigzags this one a bit, although that shouldn't surprise anyone given the show's creators. The angels are always contemptuous toward the demons, but said demons alternate—sometimes mid-conversation—between subverting this "trope", acting respectful, and (extremely rarely) genuinely being respectful toward the "heroines".
Fullmetal Alchemist has Edward Elric, the bratty teenage genius protagonist who's brash, short-tempered and swears quite a bit. He is constantly calling his opponents (and his own father) "bastard" and "third-rate novice". In contrast, the main villain, Father, heals his broken arm, inquires after his health and family, and allows Ed to live and continue his journey while he casually plans the death of over 50 million people just so he can eat God and acquire all knowledge in the universe... It makes sense in context. The Fuhrer of Amestris, King Bradley, even invites Edward and his brother Alphonse to tea. There's also Solf J. Kimblee, the Crimson Alchemist, a mass-murdering psychopath who treats Edward's mechanic, Winry Rockbell, with genuine respect and kindness while politely asking Ed to stage yet another massacre at Fort Briggs.
Played with in Dragonball Z with Frieza (prior to his Villainous Breakdown from Goku turning Super Saiyan), who generally polite with the characters fighting him. The played with part is Goku initially extends the same courtesy before Frieza kills Krillin right in front of him for no reason.

Comic Books

In Chick Tracts the angels helping the "good guys" tend to be rude and uptight, and aren't above punching sinners/devils like bullies. And many of said good guys are often condiscendent, disrespectful and arrogant to the others.

Films -- Live-Action

Dooku from the Star Wars prequel trilogy is far more polite than Obi-Wan, if not more polite than most of the jedi as a whole.

Dooku: You have fought gallantly. Worthy of recognition in the archives of the Jedi Order. Now it is finished. Surrender -- and your lives will be spared.
Windu: We will NOT be hostages to be bartered, Dooku.
Dooku: Then, I'm sorry, old friend.

In another George Lucas related movie series, Raiders of the Lost Ark, this happens with most of Indy and Belloq's interactions.

Belloq: How odd that it should end this way for us after so many stimulating encounters. I almost regret it. Where shall I find a new adversary so close to my own level?
Indy: Try the local sewer.

In Phone Booth, the protagonist is a rotten liar and the antagonist teaches him the better way to live.

Literature

The chapter "The Voice of Saruman" from The Lord of the Rings comes to mind. Saruman is (faking) pleasantness, the good guys respond harshly.
In the book The Robots of Dawn by Isaac Asimov, Elijah Baley reflects at one point how the supposed "good guy", Dr. Han Fastolfe is unpleasant and antisocial, while Kelden Amadiro, the "villain", seems friendly and accommodating. The "wolf" behind Amadiro's apparent friendliness becomes apparent to Baley later.
This sort of contrast happens a lot between Harry Dresden and "Gentleman" John Marcone in The Dresden Files. Marcone is usually polite to Harry; Harry rarely shows Marcone much respect in return, since Marcone is a mob boss. This happens a lot between Harry Dresden and practically any villain he talks to; the supernatural big bads of the Dresdenverse generally try to maintain a pretense of civility, and Harry... generally doesn't.
Galbatorix's conversation with Oromis at the end of Brisingr in the Inheritance Cycle. He tries to convince Oromis to join him using smooth speech—Oromis calls it "A balm of honeyed lies." After this, Galbatorix gives up and his voice is said to have "acquired a harsh, angry cast."
Twenty Thousand Leagues Under the Sea: This is the dynamic between Wicked Cultured The Captain Nemo and Idiot Hero Ned Land. Nemo is Affably Evil, and Ned Land doesn’t lost any chance to insult Nemo, no matter how petty. Nemo is a Well-Intentioned Extremist that maintains Ned in a Gilded Cage, and then you realize that Dumbass Has a Point.

Live-Action TV

Garibaldi vs Bester in Babylon 5. Though Garibaldi isn't really rude—he's just rough hewn.

Bester: If I had my talent working, I could have warned you when he was coming.
Garibaldi: And if I had a baseball bat, we could hang you from the ceiling and play piñata.
Bester: A piñata, huh? So, you think of me as something bright and cheerful, full of toys and candy for young children? Thank you! That makes me feel much better about our relationship.

This is the impression Chirs Sims and David Uzumeri had when they recently watched the pilot episode of Smallville: Pa Kent is a dick who eventually pushes Lex into supervillainy.

Print Media

The page image is from a Mad Magazine article parodying this trope, and for what it's worth, there are more images where that came from.

Music

From Rhapsody of Fire there are some, well, interesting lines spoken by the main hero against the Big Bad Akron in "The Mighty Ride of the Firelord", including calling him bloody bastard, spit on him and threaten to burn him and eat his brains. Granted, he has just raped to death Princess Airin and killed the warrior Arwald, but still.... They also don't exitate to refer to the Queen of the Dark Horizon as the "God-forsaken Bitch".
In the Blind Guardian song "Time Stand Still", Melkor is quite affable and polite, while Fingolfin curse him on sight.
The zombie "Bob" in Jonathan Coulton's song "Re: Your Brains" speaks as if narrating an excessively polite corporate email while trying to convince the survivors to leave their safehouse.

Theater

In the opera La Fanciulla del West, the bandit (love interest of the heroine) is kind, chivilrous, and charming, while the Sheriff of the mining post is a self-absorbed, greedy, would-be adulterer. No surprise on who gets the girl.

Video Games

Castlevania
- The opening of Castlevania: Symphony of the Night, in which Richter barges into Dracula's castle and interrupts the Count's relaxed wine(?) drinking, greeting him with "Die, monster!". He then insults Dracula, to which Dracula replies very calmly and philosophically. Richter continues insulting Dracula until he provokes a fight. Now that's rude!
- The same is true for every conversation between the protagonists and Death prior to the ending split in Portrait of Ruin.
This seems to define Edge and Rubicant in Final Fantasy IV.
In Shadow Hearts, the hero Yuri is a rough brawler; before he's given a name, he's even referred to as "Rude Hero". His main antagonist is a dapper English Gentleman with a top hat who begins battle with a polite bow.
In Bayonetta, Bayonetta is pretty flippant and mean to the angels she fights; the big bosses among them, the Cardinal Virtues, are very pleasant in conversation. Also done with Father Balder, who also maintains his manners with Bayonetta while she outright loathes him. Though in Balder's case, he crossed the Moral Event Horizon three times in one scene, and even Ax Crazy Bayonetta is disgusted by what he's done.
Part of the reason why Zero Wing was so badly translated is that CATS is using a very formal and polite form of Japanese, while the Captain and his crew are using a brusque, informal form. Even in the Translation Train Wreck, contrast "How are you, gentlemen?" with "It's you!"

Web Original

Doctor Horrible is an intelligent, respectable guy who happens to be a supervillain, while his archenemy, Captain Hammer, is basically a huge jerk who mocks the homeless. Their interactions with Penny are even more telling—Dr Horrible is genuinely interested in her but unsure of how to proceed. Captain Hammer, meanwhile, is blatantly disrespectful of her and goes after her just because it gives him one more thing he can rub Dr Horrible's face in.

Western Animation

In Amphibia, the residents of Wartwood perceive Anna as a monster, initially thinking she's going to eat them; even after Sprig befriends Anne he calls her a "monster" and an "ugly hero". Big Bad Captain Grime, however, seems to view name-calling as beneath him.