“Everybody loves celebrity children,” said Stephanie Trong, the editorial director of The Cut. “But perhaps the biggest appeal is that these guys live in the lap of luxury and they’re extremely open about their exploits. How many teens go to couture shows or fashion parties, much less document them on their joint Twitter feed, in such a hilarious, uncensored way?”

“Most of my tweets happen between 1 and 5 in the morning,” Harry said. “I’m a night owl, and random thoughts pop into my head. I’ll be watching ‘Mommie Dearest,’ and I’ll be like, ‘Oh, my God, Joan Crawford is amazing.’ ”

But this was a brief low-culture aside. For a teenager, Peter Brant can sound like a been-there-done-that dowager countess, not that his Old World pretensions aren’t refreshing in the Internet age.

“I’m interested in 18th-century furniture, late-19th-century art, the Arts and Crafts movement and history of the mid- to late-19th century,” he said. “I bounce around a lot, but I usually stick with the same three centuries.”

Harry has similarly lofty passions. “I become obsessed with things like DNA or old Valentino shows or the Qing dynasty,” he said. “I have a love of opulence.”

“They were raised surrounded by adults,” Mr. Blasberg went on. “They are fully aware of who their father is, and what art they have on their walls, and who their mother is, and what she represents in terms of fashion and glamour. Naïve teenagers these boys are not.”

“I’ve had a summer job since I was 9,” Harry said. “At our house we have stables, so I’d work in the barn. We had to clean the stalls.” Harry doesn’t share his father’s passion for polo. “I think horses are beautiful, and I respect them aesthetically,” he said, “but I can’t play polo like he does. It’s a demanding sport.”