The Tate "Ode" is an excellent poem but is it about a public tragedy? It seems more about the fear or promise of death and oblivion. It hardly matters (in the poem) that the soldiers died the way or why they did, or that their death had a social/historical aftermath.
Lowell's
Ode for the Union Dead takes a more historical and social slant to its subject.
Stylistically as well, the poems are polar opposites. I like both poems a lot, but prefer the Lowell.