By the end of 2018, the picture looked vastly different. BuzzFeed generated more than $300 million in sales, while still bleeding money, and The Times was on a pace to exceed $650 million in digital revenue.

A stormy sociopolitical climate played to the strengths of seasoned media companies. John Wagner, who handles ad spending for publisher properties for the media agency PHD, said that during the Trump presidency, advertisers had favored venerable publications like The Times, The Washington Post and The Wall Street Journal. News sites of 21st-century vintage, on the other hand, have to keep proving themselves.

“BuzzFeed has really good offerings,” Mr. Wagner said. But its listicles and quizzes, he added, may eventually fall out of favor. “Consumers are fickle, and they’ll move on to the next thing,” he said.

Mr. VandeHei of Axios said media companies needed more than digital savvy to make it in the current cutthroat environment. “I think media is still a great business, if you run it like a damn business,” he said in an email.

Mr. VandeHei recited a litany of plagues on the digital houses, such as taking investments from venture capitalists expecting big returns in a short time or tying audience growth to platforms like Facebook.

With its reliance on sponsored newsletters, Axios has a business model wildly different from BuzzFeed’s. (“I’m an outlier,” Mr. VandeHei said.) But while a comparison of the two companies may not be apples to apples, the debate over journalism’s future comes down to which business model works better — or works at all.

Axios generated more than $24 million in revenue last year while incurring an overall loss of $56,000, Mr. VandeHei said. He credited a simple reason for its success: “The audience for high-quality content is huge and voracious and growing.” And the company’s focus on newsletters means it is unaffected by the whims of Facebook.