One question is why the British allocated so few men and so little materiél to crushing the colonists' revolt. First, in the years 1776-1781 Britain had other opponents than the Continentals and was fighting in other places. At the same time that Britain was engaged in trying to catch and defeat George Washington's army, it was also engaged in related conflicts with the French, Spanish and Dutch and fighting what was to be a series of military campaigns that eventually led to British control of India. Second, the 13 Colonies were of lesser economic concern. If the Caribbean colonies had tried to become independent, the wealthy sugar plantation owners living in England (known as the Nabobs) would have pushed the government to fight much harder and longer to prevent it. Third, there was a British reluctance to get into another big fight. It had only recently finished the exhausting Seven Years' War twelve years before ( initially the American Revolution seemed to be a limited revolt by the colonists against paying for that ) and this time didn't have the Prussians to help. There were within the government voices of dissent, like Isaac Barré, who could reasonably denounce the War as a bad idea.

For the small Continental forces, there's the simple matter of population. The 13 Colonies had maybe 2.5 million people , mostly somewhat poor farmers, spread out over a very big piece of territory. They could and would only field a small force. The Continental Army they raised was never more than around 17,000- and the turnover within that was high as the War dragged on. Washington continually begged for men and supplies and didn't get them. If the French hadn't provided both, Britain likely would have won.

In contrast, the Napoleonic Wars were mostly fought in Europe, and with European forces from many European countries. Their populations were much larger, their soldiers didn't have to be loaded onto ships and sent across the Atlantic, and the stakes were much higher: for most of them, it was a battle for survival, to avoid being conquered by Napoleon.

Alan Taylor: American Revolutions