I've read where "John Brown" was originally not the infamous Abolitionist who tried to hijack Harper's Ferry, but a Sgt. in the U.S. Army during or just after the Mexican War. As with many of these military marching or "cadence" songs, many of the verses were distinctly naughty, and seem to have been lost in the mists of history.

Although the later and more famous "Battle Hymn of the Republic" is supposedly based on this earlier work, they were appantly not melodically identical. Some sources relate that they used three "Glory"s in a row instead of one in the refrain, and one recording I have heard has a distinctly different melody to the familiar meter - it could pass as, and in fact may be, a harmony line to "Battle Hymn"... or perhaps it is the other way around!
Fairly credible ACW Historians have told me that "Battle Hymn" was probably seldom heard or sung within the Union Army, and never achieved anything like the popularity of Old "John Brown". That does not inhibit me in the least, of course, from playing it around reenactment events or encampments. For a Union Unit on the march, however, I think that you would be much more authentic to stick with JB.