There are a variety of economic, political and geographic factors. Suffice to say, states that build their capitals in separate cities from their economic centers, such as the United States with Washington, Australia with Canberra, and Brasil with Brasillia, do so explicitly to separate the government from the economic and trade centers to be more objective when legislating. Understand that when the capital city of a country is also the most powerful economic center, such as Paris in France or London in Britain, the city isn't economically successful because the government is there, the government is there because the city was economically successful in the first place.
From an economic and population standpoint NYC has a few things that historically recommend it over DC. The first is obvious, New York had over a century head start and was already one of the trio of large Mid Atlantic and Northern cities that had separated themselves along with Boston and Philly.
The second is geography. NYC is one of the great natural harbors of the world, with sheltered anchorages from Staten, to Jersey City, up to Manhattan, Jamaica Bay and off Brooklyn. While it offers easy access by the East River up to Long Island Sound, or on the other side up the Hudson. And that is a key part. Much of the early industrialization of America occurred in along the Hudson, in places like Albany, while the Erie Canal connected the Hudson to the Great Lakes, allowing the goods and shipping of the entire Mid West to flow down to New York City. And for all the swampy land in what makes up the 5 boroughs today, DC was still far worse far more recently. Much of the what is today the National Mall is reclaimed land for instance.
DC meanwhile had a FAR smaller amount of valuable shipping coming from up river, most agricultural products from Western Maryland and the Shenandoah river valley. Indeed the location of Georgetown and Alexandria both predate DC and are there for a reason. It is essentially the furthest that a sizeable vessel can navigate up the Potomac from the Chesapeake. Beyond them sit the Great Falls which saw some early attempts at canals, but which always limited the amount of commercial shipping that was going to drive development in the region. Indeed the Potomac is also mush more difficult to navigate than the Hudson, and more dangerous for vessels as well.
The final is the small size of the federal footprint for the first century of the city's existence. The large federal workforce simply wasn't really a thing until the 20th century. Even as late as 1888 the War, State, and Navy Departments were able to fit into a single new building, the Old Executive Office Building though they did outgrow the arrangement after a decade or so. While today the large part(but still a minority) of federal govt employees do much to drive the DC economy, and corporations find it worthwhile to plan and add locations to directly serve govt customers the dynamic simply wasn't true even 150 years ago.
Hence the two competing centers of power like in so many other nations and states between the newer planned center of govt, and the older organic center of economic activity.
In addition to the wonderful answers the other commenters have given, I would add the following 3 notes:
New York was at one time the capital.
By being a district separate from any state, DC is impartial and no state has jurisdiction there. (Or, you know, that's how it's supposed to work.)
The Compromise of 1790.
edited: formatting