For many tourists, the first order of business on their maiden visit to Manhattan is to overcome a slight sense of disappointment. Rather than seeing the endless avenues of ultra-modern skyscrapers that they were promised, they are greeted by old-fashioned neighborhoods of unremarkable height, whose size and rhythms have more in common with the Old World than with that mechanized metropolis that haunted the dreams of the modernists.

There is, however, one city, literally on the other side of the earth, that comes far closer to that mythic Manhattan than Manhattan does itself. It is Hong Kong, the subject of “Vertical Cities,” a new exhibition at the Skyscraper Museum, comparing the two metropolises. Like New York, Hong Kong, with its 7 million inhabitants, is one of the densest cities on the planet. But unlike the people of New York, a city whose density is somewhat spread out, or Cairo, whose density — the greatest in the world — is crammed into low-lying tenements, Hong Kong’s citizens live and work and shop in high-rises.