Both Boston and New York City are incredibly important early settlements that still thrive to this day. Given the early advantages of Boston I would assume that it would be one of the top 5 largest cities in the USA, however it is only ranked as the 21st largest. New York City has at least 13 times the population of Boston. What has led to this large disparity between New York City and Boston? Are they simply geographical limitations or are the reasons ultimately political/economic/cultural in nature?
Don't confuse the concepts of incorporated city, which has more to do with state statutes and regulations in regard to municipal consolidation, with metropolitan area, the true size of the municipal economic entity.
The least biased statistical evaluation of municipal areas I could find for the U.S. is The List of Combined Statistical Areas (2010 Census) published by the United States Office of Management and Budget here and partially reproduced below, in decreasing order by population:
As you can see Boston-Providence occurs 5th, as your initial estimate expected.
Updated to 2010 Census - Boston returns to 5th place
The defining characteristic of New York City has always been its harbor, today formally known as The Port of New York and New Jersey... one of the largest natural harbors in the world... It includes the system of navigable waterways in the estuary along 650 miles (1,050 km) of shoreline in the vicinity of New York City and northeastern New Jersey, as well as the region's airports and supporting rail and roadway distribution networks.
New York harbor is a very large deep water port that can accommodate numerous deep water/high tonnage ships. It is through New York Harbor that the waves of immigrants came to the USA in the 19th and early 20th Centuries. Ellis Island is in New York Harbor.
The immigrants came to New York City through the harbor and settled in the city, and its population grew and grew and grew. At the same time, the port served as a center for commercial trade, bringing in raw materials including coal, iron, timber, and numerous other materials from East Coast of the USA and from overseas, that allowed industry, manufacturing, and large wholesale and retail businesses to flourish. And via the port, businesses also had an easy route for shipping their goods to those same destinations.
This made NYC a dynamo of trade and industry that supported the ever increasing population that came in through the harbor, and then settled and raised families in the great city.
NY Harbor dwarfs Boston harbor, which is listed officially as comprising only 500 acres. That is the simple, obvious answer to your question.
(My apologies for lack of more references at the moment. As a native of New York City, this knowledge is intuitive to me - I learned it from my father, whose parents came to Ellis Island; I learned it in grade school and in high school and I live with it every day, my home being only blocks from the shores of the great harbor itself)
The Erie Canal via the Hudson River to the Great Lakes gave New York access to a much larger hinterland. Boston has the Charles River and not much else.