Wellington had two enormous advantages over the french in the Penninsular Campaign, which were the difference between victory and defeat (1) the Spanish and Portugeuse Guerillas who harried the French supply lines, and (2) the fact that his light infantry was armed with rifles, while the French Voulitgeurs (why did the French call their light infantry Vaulters?) had only smooth bore muskets.
Were Wellington to have fought a major campaign in the southern United States, the Americans would have had these advantages, not Wellington. Further, as Wellington was want to ride his horse along the battle lines, and American sharpshooters were encouraged to kill any enemy officers in range, it is highly unlikely that Wellington would have survived his first attack on an American position. The British fighting in the United States in the Revolution and the War of 1812 were in the same position as the French in Spain and Russia, The British in Afghanistan (when 5 troops out of a 10,000 man force under Elphistone made it back to India in 1842), the Nazi's in Russia, the Russians in Afghanistan or the United States in Vietnam or Iraq: a hated occupying force whose every soldier was a target of opportunity for the populace they would have to subjugate.
And for these very reasons the American invasion of Canada during the War of 1812 failed miserably.
Similarly, when after an American gunboat siezed two Confederate envoys off a British ship, and the Hawks in Paliament wanted to send Sir Garnet Wosely with 50,000 men (most of whom had never heard a shot fired in anger) to invade New York from Canada during the Civil War, (had Lincoln not released the envoys) that expedition would have ended in disaster. Could you imagine 50,000 troops who had never faced a foe armed with anything more menacing than an Ashanti tribesman's spear marching a couple of hundred miles through thick woods while being sniped at constantly, only to face a pitched battle with 100,000 veterans of Antietam, Gettysburg, Fredricksburg and our Peninsular Campaign in Northern Virginia on ground of our chosing in upstate New York? Anytime you have to attempt to take and hold a hostile country, with exposed supply lines, facing guerilla tactics as well as expert marksmen who are capable of decimating your officer corps, you are not going to win. Period.