Hi Rushton - many people do say that Copland is the most American of composers. He is certainly the most popular, and his music is the most accessible, and he helped define how much American music sounded afterwards, especially in the realm of film music. He did write a great deal of music that had American history as the theme, too.
However, Ives actually used quite a bit more of American folk tunes than Copland did, and was very original, experimenting with bi-tonality pretty much before anyone else did, and with quarter-tones, etc. He was very largely self-taught, after the instruction his father gave him, unlike Copland, who was heavily influenced by the European tradition, having studied with Boulanger and others over there. At least as much of his music was American themed as Copland, as well. So for those reasons I would argue that Ives is more quintessentially American as a composer than Copland. It is an interesting debate, to be sure.