Both editions were used during the war. While the 1862 is an update, many officers only had the older book. Also, some units only had 2 band rifles (Mississippi Rifle) so they didn't even need the update.
On the Union side, Hardee's was replaced by Casey's rather quickly. (Not very patriotic to reference your enemy's book :-) So, pretty much only use Casey's for the Union side. The 3 volume Casey's is also very useful for wargamers in that it covers larger formation movements, brigade, division, Corps (both side's practice in the war) considerably better than either Hardee's book.
Of lesser use, but still interesting is the officer and NCO pocket companions. I believe both are still available in reprint. They were written toward the end of the war, but cover allot of the actual field practice used during the war. Great references for siege defenses, camping, cooking, guard duty, skirmishing, etc.