David Letterman and John McCain David Letterman and John McCain

John McCain and David Letterman are two of the country's biggest grouches, and they'll face off this week in the ultimate cranky battle. Or make nice. We're not sure yet. Sometimes their grouchiness works for them – McCain says he didn't go to Washington to win Miss Congeniality – and sometimes it turns people off.

The two have a lot to talk about after McCain skipped out on Letterman last month to sit down with Katie Couric. Here's a look at their respective feuds through the years, and who came out on top:

McCain vs. Paris Hilton: When McCain included Hilton in an ad deriding Barack Obama's celebrity, the heiress made a video questioning McCain's credentials: "He’s the oldest celebrity in the world… Old enough to remember when dancing was a sin and beer was served in a bucket."

Winner: Hilton. But that just plays into McCain's case that Obama's the candidate of dippy celebrities.

Letterman vs. Paris Hilton: Soon after Hilton's release from jail, Letterman sat her down to ask: "Which do you prefer, New York City or Los Angeles? Mm-hmm… How'd you like being in jail?" Hilton, after four minutes: "I've moved on with my life, so I don't really want to talk about it anymore." Dave: "See, this where you and I are different, because this is all I want to talk about."

Winner: Letterman   

McCain vs. The New York Times: After a series of unfavorable stories and perceived mistreatment, a McCain advisor said the Times is "not by any standard a journalistic organization. It is a pro-Obama advocacy organization that every day attacks the McCain campaign, attacks Gov. Palin and excuses Sen. Obama."

Winner: McCain builds his conservative bona fides with people who despise the Times.

Letterman vs. Rush Limbaugh: On the Late Show, Limbaugh said Hillary Clinton resembled "a Pontiac hood ornament" in a recent photo layout. Letterman: "You can say that because you are the finest-looking human specimen on the planet." Letterman later proposed they wrestle, and finally asked, "Do you ever wake up in the middle of the night and just think to yourself, 'I am just full of hot gas?'"

Winner: Letterman

Letterman vs. Jay Leno: Letterman left NBC for CBS when Leno beat him out as Johnny Carson's replacement on "The Tonight Show." Since then, Leno has won consistently in the ratings.

Winner: Leno, if you go by ratings, but Letterman's booked presidential candidate McCain, and Leno only has VP nominee Joe Biden.

McCain vs. Donald Rumsfeld: The Arizona senator said in December 2004 that he had "no confidence" in Rumsfeld, nearly two years before the Defense Secretary's ouster, citing his handling of the Iraq war and a troop shortage. McCain backed the surge, and many credit it with improving things in Iraq.

Winner: McCain

Letterman vs. Oprah Winfrey: For years, rumors circulated that Letterman and Oprah didn't like each other. Maybe it sprung from that "Oprah… Uma" deal when Dave hosted the Oscars. Anyway, Oprah came on their show, they had a great talk, and everything's cool.

Winner: Everyone in America

What do you think? Will McCain and Letterman continue their spat, or make up?