As the story goes, the Dutch thought Suriname would be worth more; and we chuckle to ourselves, knowing how obviously wrong that turned out to be. The implied value of New York in this retelling turns out to be its location: it has natural harbors and was smack dab in the middle of all the European coastal colonies, so it's great for trade, and in fact goes on to become the financial capital of the planet.
But how much of this value is also due to scale? That is, the fact that once it was incorporated into the British Empire, it benefits from access to friendly neighbors and collective infrastructure. Would New Amsterdam ever have had anything close to the same amount of value if it remained a small Dutch island surrounded by the English? Or would the Dutch Empire have found itself in a Portugal situation, sinking money into supporting unsustainable and unprofitable colonies that eventually succumb to bankruptcy, rebellion, or conquest?
Edit: just realized that this post is framed as kind of an alternate history question, which is really unanswerable, and also in the long run almost every European colony achieved independence one way or another. So to put it a different way: at the time of the transfer, did leaders of either the British or the Dutch openly acknowledge that in the long run, Manhattan could be valuable for the British, but not for the Dutch?
Without needing to evaluate the hypothetical, we can say that swapping New Netherland (which was considerably larger than just Manhattan) for British territories in the Caribbean was a great trade for the Dutch.
While it’s hard to imagine today’s New York being unprofitable, the Dutch colony based on Manhattan and Albany (then, Nieuw Amsterdam and Rensselaerswyck) bled money throughout the sixty-odd years of its existence. The kind of place that New Amsterdam had already started to become simply wasn’t a good fit for the Dutch colonial model.
It’s worth taking a step back here to consider what the European powers were doing in the new world in the first place. France, England, Spain, Holland, and Portugal (plus Sweden, Scotland, and Denmark in a small way) all had colonial activities in the new world, but each of these empires operated differently. The English, for example, had two distinct types of colonies: settlement colonies such as those in mainland North America, which were mainly places to settle down and live, and extractive colonies such as those in the Caribbean, which relied on slave labor to maximize profit without any real interest in establishing a long-term settlement.
The Dutch generally favored trade-based colonies that used small contingents of Dutch regulars supported by mercenaries and locals to control high-value trade goods. Most of the imperial powers had chartered trading companies, but the Dutch East India company was the largest of the lot. The fabulous wealth of the Dutch empire came from a network of small, tightly-run outposts controlling trade throughout Sri Lanka, Indonesia, and Southern Africa.
New Netherland was supposed to work on the same basic principles - reading not for spices, but for fur. Almost immediately, the West India Company ran into problems getting their money’s worth out of the settlement. It’s position on a natural harbor with large amounts of agricultural land nearby attracted settlers from all over the Atlantic world, and those people had no interest in generating profit for stockholders in Amsterdam. Within a decade or two, Nieuw Amsterdam had stopped being a fortified trading outpost and become something like a real city.
After a series of drunk, corrupt, and generally unpopular directors, the company attempted to restore order by installing a by-the-book military administrator (and a fire-breathing Calvinist to boot) in the form of Peter Stuyvesant. For the people of the colony who had become accustomed to a degree of benign neglect, this was the last straw. Led by the town scout (a sort of combination sheriff and magistrate), a group of influential settlers petitioned the Dutch authorities to remove Stuyvesant and implement some form of representative government. They actually succeeded in securing some concessions, though it was only a few years later that a defanged Stuyvesant surrendered the city to a British fleet.
So, in summary, the Dutch knew what they were getting and managed to wring some profit out of a hopeless situation. New Netherland was an experiment gone embarrassingly wrong for the West India company - a trade enterprise that never once turned a profit but did attract malcontents and mutineers. The sugar and spice output of Guyana and a few Caribbean islands were, at the very least, reliably profitable and free from the administrative headaches of running a city on a foreign continent. It was a deal taken at sword point, but not an entirely unfair one.
Source: Russel Shorto’s The Island at the Center of the World.