We did both a couple of weeks ago and had a great time at both. I guess it depends on which type of show you prefer. The food is very similar- creamy vegetable soup, roll/biscuit, chicken. The BBJamboree had ribs and a chocolate mousse type dessert, while the Dixie Stampede had a piece of pork tenderloin, and an apple turnover dessert. Dixie Stampede doesn't give you silverware. BBJamboree offers chicken fingers for the kids.
The shows are completely different. BBJamboree is singing and dancing, with some Country Bear Jamboree type bears on the sides of the theater that tell jokes and interact with the performers. You eat before the show. If you can, get a table close to the stage. DD6 was right next to it, and loved seeing everything up close.
Dixie Stampede is more of a rodeo. You sit in a row at long tables and they bring each food out to you one by one. There's lots of horseback riding and tricks, longhorn cattle, ostriches, chickens, pigs, and more, and the audience participates by being on the North or South side and cheering the performers on. It's more expensive than the BBJamboree, and while we were there, kids were free at BBJamboree. Like I said, we loved both, but if I could only do one, I think I'd pick the Dixie Stampede, but that's mostly because DD is an animal lover.