Hey, I'm currently doing my dissertation on Wellington's Army in the Peninsular! However, in my reading, I've also come across significant writings on Britain's split effort between North America and the Peninsula.

My sources for this include Britain Against Napoleon, released this year, by Roger Knight, Wellington's Army, by Charles Oman, The War of Wars, by Robert Harvey, aswell as Wellington's dispatches, his general orders and some correspondences between himself and Lord Liverpool I was able to view this year.

Short answer; the British put far more effort into the war in the Peninsula, both in terms of finance, manpower, effort and time. You see, while the War of 1812 was important for instances of trade, national prestige, naval manpower and strategic thinking, the Peninsular campaign had very wide effects for Britain in the European theatre; I do not like to over exaggerate the 'Spanish Ulcer's' effect on toppling Napoleon. However, it was very key to British morale, to draining French resources, and encouraging other Continental powers to defy the French - a major factor, but not an overarching one.

A point of evidence is that, of the 186 infantry battalions available to the British Army from 1809 to 1814, about 75 were deployed to the Peninsular at any one time (Oman), while roughly 120 saw service there (also Oman). Compare this to the North American theatre, where the troop numbers were far lower; as few as 11,000 men fought at New Orleans.

In truth, the War of 1812 was a sideshow. It was a diplomatic miscalculation by the mediocre Spencer Perceval, that the following ministry was unable to deal with as it's attentions were devoted in huge amounts to Napoleon. It's effect, however, was actually quite key; it made it difficult to acquire solid specie (physical currency) for expenditure on the continent. The limiting of Anglo-American trade closed off a valuable market to British taxes, and though it was far from a gigantic hit, at a time when the British ministry was doing an incredible job of clawing for every last penny to send to the Continent.

The latter part of your question is certain; militarily, financially, diplomatically and rhetorically, the UK put more effort into fighting Napoleon in Portugal and Spain than in fighting the United States. However, the brief conflict did have a small effect on the British as it limited trade, already severely hampered by the French Continental System, and decreased the value of British contributions in the eyes of some (few) Austrians, Prussians and Russians.

If I could summarise poorly, the War of 1812 was a mistake, the Peninsular Campaign was an endeavour.