As many have already said Wellington fights only on Wellingtons terms.
And as already posted in this thread, while Wellington stated he'd accept a command in North America he also felt he wouldn't be able to much more there than was already being done.
His army are highly trained an highly experienced veterans of a war fought against the best armies and keenest tactical minds of Europe and maybe even the world at this point.
You do realize that nearly all of the UK troops and commanders facing Jackson were veterans of the Wellington's army in the Peninsular campaign? The UK force's main problem was hubris;
"We beat Napoleon so slapping around these assclowns will be easy..."
Napoleon is to jackson as Andre the Giant is to a dude with one year of Karate classes at the Y under his belt. Even if the Kentucky militia are better individual shots than Wellingtons troops, the British and more specifically Wellington are far better at Warfare.
I happen to believe that is Pakenham had been able to reach his new command earlier, Jackson would have been forced to abandon and burn New Orleans. As it was he arrived far too late to much effect the campaign and was forced to play a hand which was already dealt.
I'd expect people to have a better grasp of the situation.
The US of War of 1812 has over twice the population of the colonies during the Revolution, is far larger geographically, and is far more developed while the UK is using far fewer troops than it did during the Revolution with far less local support. Thanks to the RN, the UK can land almost anywhere in the US it wants and burn almost anything it wants but the UK cannot maintain any presence ashore for any lengthy period of time. The US was simply too big and the UK forces employed too small for any lasting effect. The Chesapeake campaign, where the UK forces at New Orleans had been fighting earlier, showed both those handicaps in spades.
From mid-1813 until the war's end, the UK stooged around Chesapeake Bay accomplishing little beside launching a few punitive raids. While RN basically sailed wherever it wanted to, UK forces ashore had a somewhat different experience. An attempt on the Norfolk shipyards failed because the UK didn't have enough troops on hand. A later attempt on another shipyard further up the Bay failed for the same reason. The UK did put 5,000 or so troops ashore, slap around a scratch US force at Bladensburg, and burn Washington, but that raid accomplished nothing. The UK attempt at the real strategic target on the Chesapeake, Baltimore, was countered easily by the US for several reasons not the least of which that the UK was outnumbered by more than three to one.
Simply put, the UK can hurt the US here and there but it cannot land a knockout blow. Both sides pretty much realized this and that's why the war ended in what can be described as a win-win: Canada remained in the empire and the UK finally withdrew from the Old Northwest.