When the mocker takes on the talker

It's always easy to tell who has the upper hand in a rivalry: The loser cares a little bit more. (Just think about the Red Sox and the Yankees. Or don't, if it makes you feel better.)

So it was telling, and not entirely surprising, to see how much Stephen Colbert made of Thursday night's TV matchup, in which he and Fox News Channel host Bill O'Reilly -- the parody host and the object-of-parody -- did guest spots on one another's shows. The giddy crew on Comedy Central's "The Colbert Report" had packed the set with such props as a "Bill O'Reilly Advent Calendar" (with Colbert as the Virgin Mary and O'Reilly as baby Jesus), a portrait of O'Reilly in a gilded frame, and a "Mission Accomplished" banner, perhaps the ultimate signpost of our times.

And what, exactly, could have been accomplished? The segments in question -- which took up 20 minutes, total, on both networks -- didn't provide uproarious humor. They did prove that Colbert's show has cultural legs; even the haters are curious, it seems. And they gave O'Reilly a chance to earn a grudging respect from Comedy Central fans. The man knows he's being mocked, but agreed to play along; he showed a likable sense of game, if not a stellar sense of humor.

Colbert's jokes, truth be told, fell a little flat, as well, but that seemed to be a flaw with the scenario itself: Because his TV persona is one giant O'Reilly joke, there wasn't much more that needed to be said. On "The O'Reilly Factor," Colbert was reduced to fairly obvious lines like, "I want to bring the message of love and peace to a younger audience: People in their 60s, people in their 50s. People who don't watch your show."

O'Reilly, for his part, seemed to view the experience as an anthropological experiment. He tried his hand at a Colbertesque interview; his first question was, "Colbert. That's a French name, is it not?" and his fourth or fifth was, "Don't you owe me an enormous amount of money?" And when the segment was through, he convened a panel of media critics to explain what this "Colbert Report" phenomenon was about.

It was striking, actually: Bernard Goldberg , perennial critic of the "liberal media," waxed nostalgic about the days of Lucille Ball , when comedians merely laughed about themselves. He's right that Colbert and Jon Stewart are experts at mockery, and that snarkiness fits a particularly modern sensibility. (He failed to mention that parody itself has been around a lot longer than "I Love Lucy.")

But he missed what makes O'Reilly such a fascinating figure, and what Colbert manages to nail so completely. The Fox host is the polar opposite of self-deprecating; on TV, at least, he seems constitutionally incapable of self-criticism, or even self-reflection. At the end of Thursday's "Factor," he read an e-mail from a viewer: "Bill, do you think you have ever been wrong?"

"I know I've been wrong, Steve. I read your letter," O'Reilly said. Then he smirked, partly because he was kidding, but partly because he was proud.

He reprised the joke on "The Colbert Report." And in terms of sheer timing, it may have been the best line of the night.

"We make mistakes," Colbert said, O'Reilly-like, "but we never admit mistakes."

"We should admit them," O'Reilly replied. "This was a huge mistake, me coming on here."

The audience howled, in deep appreciation.

Joanna Weiss can be reached at weiss@globe.com. For more on TV, go to boston.com/ae/tv/blog.