From the ads on Times Square to the 21-gun salute on the White House lawn, everything about President Hu Jintao's visit has been designed to show that China has arrived as a major world power, and its leader deserves to be treated as an equal.

China's state-controlled newspapers and television channels were dominated Thursday by images of Mr. Hu and President Barack Obama, side by side. The official Xinhua news agency characterized China and the U.S. as "two heavyweight players on the international stage [that] have seen their national interests increasingly interwoven." China Daily added: "The rest of the world has been paying close attention to every word and gesture—given the importance of the two countries to the global economic and political landscape."

Even as many Americans appear convinced that China is about to overtake the U.S. economically or militarily, state media outlets called for deeper relations based on mutual respect. The bi-weekly World News Journal said the U.S. should adjust its mentality of "deep suspicion about China." Other publications called for the end of a "zero-sum game" mentality.

More broadly, on the Internet and Beijing streets, many Chinese appeared uncomfortable about their country's newly feted status as an emerging superpower—or were nonplussed by the coverage.

Several comments online expressed skepticism about China's portrayal as an emerging superpower. "Looking at those high-profile reports on Hu's visit by major media, and with TV all about how harmonious and wonderful this China-U.S. relationship is, it's just way too phoney," wrote a user called Mahua-apsaras on the Sina micro-blogging service.

Another online user pointed out that despite its status as one of the world's largest economies, China's economy is roughly one-third the size of America's. "Do not give China a big hat, we are a poor country," the user wrote.

Many Chinese citizens have a nuanced view of their country's place in the world and its relationship with what is still the globe's dominant power.

Liu Wenhong, a bespectacled 45-year-old who has made and lost a small fortune twice over the past 20 years, illustrates the ambivalence. "I don't think China is that powerful or a threat," he said, adding that he hasn't had time to read a newspaper or watch a television report on Mr. Hu's visit. "You're only seeing a quarter of China. The majority of China is still underdeveloped. We're all busy taking care of our own businesses."

Mr. Liu's own experience is proof of how dramatically Chinese perceptions of their own country and its relationship with the U.S. has changed since diplomatic ties were established in 1979.

During the 1966-76 Cultural Revolution, Mr. Liu recalls, he was taught that all Americans were "imperialists"—though he says he didn't know then what the term meant. He remembers Mao Zedong denouncing the U.S. as a "paper tiger."

In a new era of economic reforms, Mr. Liu sold clothes, traded coal, and, inspired by a book called "The American Dream," invested and lost his savings in the stock market. He started trading coal again, and lost his savings again when prices plunged in 2008. Now he sells fresh natural yogurt for three yuan (less than 50 cents) a pot from a street-side stall in downtown Beijing.

He still admires many aspects of the U.S. system. But he is no longer in its thrall, and is sometimes irked by what he perceives as U.S. interference in China's affairs. "The U.S.'s arm is extended too far," he said. But of China, he added: "They say that the sleeping lion is waking and putting pressure on the entire region. I don't think that's the case."