The WWII Museum is really terrific. Even non-history buffs will find it illuminating and fascinating (and very moving). I particularly like the oral histories that are found throughout the museum (not to mention that there are often veterans there, visiting or volunteering, who will gladly share their personal stories). A friend of mine was shocked to find his father in a photo there. It's also very extensive: you could probably spend a couple of days exploring and delving into the dense exhibits. SO if you have a particular interest in WWII, you can't go wrong. And American Sector, the John Besh restaurant on the premises, is terrific (great happy hour specials too).
That said, you're IN New Orleans, so first and foremost you should absolutely tour the French Quarter and explore the local history. There are some good niche tours that explore different aspects of the local history. In three days, though, you ought to have enough time to do some of both. It's true that you could spend days at the WWII museum, but you could also just spend a few hours or a half day doing a chunk of it (it's well laid out, with exhibits focusing on specific battles, regions, and subjects), leaving time for other touring and exploring. And eating and drinking and music, needless to say.
I guess while you're working through this decision, mentioning the Civil War museum isn't a good idea??
Here's one thing that might make your decision easier: depending on when you're visiting, you might run into serious heat and humidity, or buckets of rain. Hellooo nice, dry, air-conditioned museum with good restaurant!!
Good luck and report back after your trip - would love to hear what you think.