The Light Infantry gunpowder tree of units counteracts Heavy Infantry, and all Light Infantry also counteracts the Archer tree.
Other bonuses are more subtle, such as the Chinese UU being a gunpowder unit a whole age early in Age3. In terms of pure fighting prowess, I'd say the American UUs give the biggest battlefield advantage of any UU in the game - but like OP says, this still boils down to a couple of pluses to a few traits. The American UUs, in addition to the nationwide +2 to resource collection, also get an HP bonus, an attack bonus, and they automatically entrench. The Bantu, for instance, have early Age1 UU infantry that can outrun all units except cavalry (an Age2 unit) so they can wreak havoc when raiding.
Some UUs have odd powers that can be much more influential on a game than others.
