While New Orleans was one of hubby's and my favorite places to visit, and we've been there many times, I must say the Grand Canyon is spectacular and totally unique. I have never ridden the SWC so I don't know about the scenery along the route, but others here say it is good.
Washington, DC, is packed with American history, of course. The Crescent goes through lots of forests on its southward journey. The ride across Lake Ponchartrain is interesting. Some of the charms of New Orleans are the history, architecture, food, and nightlife. Between the two (New Orleans and the Grand Canyon) for a one-time-only visit, I personally would choose the Grand Canyon. Just my opinion, of course.
I have been told that the CZ is the most scenic of the westbound trains from Chicago, but that of course is a matter of opinion. I've never traveled any of them, but I hope to take the CZ sometime later this year.
As someone already posted, amsnag.net is a very helpful website that shows the different fares for different dates, depending on how many tickets have already been sold. It might save you some money if your dates are flexible.
Best wishes for a fabulous trip!