The capture of the USS Chesapeake was one of many small-scale naval engagements of the war which didn't have much strategic impact on their own. The only naval battle with decisive consequences would probably be the Battle of Lake Erie.
As for the American Revolution, the British Empire was using its full naval and land strength in an attempt to crush the rebellion. During the campaign to take New York Britain sent 32,000 troops and even had to supplement its strength by borrowing regiments from German princes in exchange for money. Even during the Napoleonic Wars there were only about 40,000 British troops in the peninsular campaigns and a similar number in the Waterloo campaign.
In the American there were several catastrophic defeats which convinced parliament to end the war after eight years of fighting. During the Saratoga campaign about 14,000 British troops were involved. More than 10,000 were lost and Burgoyne's army was forced to surrender. Cornwallis surrendered with about 9,000 troops at Yorktown after an extensive campaign.
In the War of 1812, Britain did make a big effort again even though the Napoleonic Wars had been so expensive. Some 5,000 troops were committed to the Maryland campaign which ultimately ended in failure. Pakenham had about 11,000 troops when he was disastrously defeated at New Orleans.
*Edit P.S. During the revolution the colonists considered themselves British. Paul Revere actually said "The Regulars are coming" not "The British are coming." I disagree with modern writers calling the rebels "Patriots" because at the time they were just the opposite- traitors. To call them "Patriots" would deny that the war was a revolution rather than a war of independence against a "foreign" overlord.