For the War of 1812, British and Canadian troops wore pretty much the same as in Europe. There was a change in progress, and you'd have to check what was correct for a particular unit. Most obviously, the shako changed to the "Belgic" type, worn by troops at Waterloo. I'm not so well up on US troops, but if you're not getting too close, some non-US figure might pass with the correct uniform colour. Osprey Publications are one of the first places to look to find a starting guide to uniforms.