Either of them might be right, it depends on exactly what you ask. You don't need to worry too much, as a History Editor can move it to the best spot if they think you didn't find it. (I'm not a History editor, though - one of them night be able to give you a different answer to find where American War history questions go. I don't see anything obvious, assuming you plan to cover multiple wars.) Basically, think about the players you expect to be looking for it - are they more likely to be thinking American History, or War History? This will affect the number of players who find and play it in the long run.
Once you have chosen the category, you can refine the exact wording of your questions and information for the target audience.
(Editor, Humanities, Literature and Books For Children)
That's all, folks!