In my view, the Market Revolution that began not long after the War of 1812 was more important in changing the American economy than the Industrial Revolution that began a little bit earlier. Together, the two revolutions changed the American economy dramatically by 1860.
By 1860, the US economy was much more diversified, much more market-oriented, and much more interconnected than it had been in 1800. This is due mainly to the two revolutions mentioned. In 1800, the US economy was much more agrarian than in 1860. In 1800, most people were farming for subsistence and were not really buying much of anything with money. By 1860, money dominated the US economy and there were relatively few people who were growing or making almost all of the things that they needed. In 1800, land transport was very difficult and water transport was confined to oceans, large lakes, and navigable rivers (where it was much easier to transport things downstream than up). By 1860, steamboats and canals had created a much broader and more effective water transport network and railroads had drastically reduced the cost of land transport.
In my view, the Market Revolution was somewhat more important than the Industrial Revolution in making this all happen. It is true that the Industrial Revolution created the steamships and trains that created a large, interconnected economy. However, this transportation network would not have had much to transport without the Market Revolution. Before the Market Revolution, people were growing their own food and making their own cloth. If they needed something they could not make, they probably bartered with a neighbor for it. If this system had continued, there would have been nothing for the trains and steamboats to transport. The Market Revolution created a need for goods to be transported from producers to consumers. This, in my view, makes the Market Revolution slightly more important than the Industrial Revolution in creating the new American economy in the first half or so of the 19th century.