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.

Like New York City, Hong Kong began as a colonial trading post on an island blessed with one of the great harbors of the world. But, as this exhibition illustrates with maps, panels, and mock-ups, there is one all-important difference. Manhattan is almost entirely flat and as such could easily accommodate the grid plan that was promulgated in 1811. Hong Kong, by contrast, is surrounded by steep mountains that intrude, delightfully but inconveniently, into the very heart of the city. A consequence of this topological oddity is that much if not most of the available land is beautiful to look at, but not especially suitable for development. This means that the city’s 7 million inhabitants are compelled to crowd themselves into narrow high-rises where space is available.

As for the buildings themselves, some are better and more daring than most recent New York skyscrapers, while some are far worse. In the latter category are mostly residential developments intended for the middle and working classes. To judge from the images displayed at the Skyscraper Museum, these do not appear to be making the slightest effort at beauty. Indeed, to call them architecture or design at all is probably better than they deserve. Rather, like some of the white brick buildings that marked Manhattan and the outer boroughs in the 1960s, they have been created unapologetically according to formula, with so many rooms, bathrooms, terraces, for the money. The one saving grace of Hong Kong is that its natural surroundings are so grand, and its buildings are sufficiently spread out, that even the less affluent tend to have views that would be the envy of many a Manhattan millionaire.

At the same time, there are some genuinely distinguished skyscrapers in Hong Kong, whose detailed three-dimensional models are on view in this exhibition. One of the more remarkable aspects of Hong Kong high-rises is that they tend to be far more slender than their Manhattan counterparts. Whereas a slenderness ratio of 1:12 is fairly standard in New York, in Hong Kong 1:20 ratios are not uncommon. Now a ratio of 1:20 is truly thin, its dimensions recalling a no. 2 pencil more than a tower. Regarding the three models on view, it is worth noting that each is by a firm based in New York. One of the most distinguished of these is the Bank of China Tower (1990), by Pei Cobb Freed & Partners, an astonishing game of facets and fractured cubes that yield a rare serenity.

Another worthy building is the International Finance Center (2003), designed by Pelli Clarke Pelli Architects, the firm that brought us the World Financial Center in Lower Manhattan, as well as, across the Hudson, the Goldman Sachs Building. In fact, in its slightly historicist references to the Art Deco skyline of the 1930s, this firm’s Hong Kong project bears a striking resemblance to the one in Jersey City.

Scheduled for completion in 2010 is Kohn Pedersen Fox Associates’s International Commerce Center. At 1,588 feet, it is set to be the tallest building in Hong Kong. In the model, it looks like a tree trunk that exfoliates into four leaves around a central axis: a more daring move, doubtless, than the architects would have attempted here in New York.

To judge from “Vertical Cities,” Jane Jacobs wouldn’t stand a chance in Hong Kong. Popular sentiment may evolve in years to come, but for the time being, the citizens of this magnificent port want and expect to live above the ground. And whereas New Yorkers tend to see infrastructure as a necessary evil, the citizens of Hong Kong positively revel in their roads and subways, in escalators that rise up the side of a mountain, and bridges in midair that link one high-rise to another.

In some respects, the collective attitude of the citizens of Hong Kong to their ultra-modernist surroundings recalls that of New Yorkers four decades ago. The marketing brochures and paraphernalia on view at the Skyscraper Museum suggest an innocent embrace of height for its own sake, with none of the anguished self-questioning that has been part of New York’s urbanistic debate for many years now. Hong Kong is witnessing the stirrings of a preservationist movement — such as emerged here in the wake of the 1963 destruction of Penn Station — but as yet it is almost unformed, and it will be years before Hong Kong’s all-mastering impulse to build up is reversed.

Through February (39 Battery Place, between 1st Place and Little West Street, 212-968-1961).