The British army really had a lot of highland Scots in those days. Probably the only way a lot of them could earn a living. It was the Black Watch along with the Hessians who defeated Washington in New York.
Although they were fine fighters they could be beaten when poorly led. For instance at New Orleans. Of course a lot of Jackson’s men (and Jackson himself) were Scots Irish backwoodsmen.
I was reading an article about the Black Watch the other day and found it interesting that they refuse to display the battle honors they received from the American Revolution, for they “do not honor battles against kith and kin”.