My personal favorite by far in the Huntsville area is Chuckwagon (located in Madison, which is just west of Huntsville city limits). Pork and brisket was excellent last time I tried it. Moe's Original BBQ is decent, I like their smoked wings and turkey, pork is good too. The Greenbrier restaurant that I call the "old" restaurant is still open. It's the one I remember going to as a small child (I'm 49, BTW). It's located in the middle of farm land with an old (active) cotton gin next door. It's pretty good, they also have really good catfish and serve all you can eat hushpuppies that are GREAT. The place looks like a dump from the outside, but it's good. The Greenbrier that actually burned down was in a newer commercial style building on a service road of I-565, which is no longer in business.
I've lived in Decatur all my life and I would not recommend Big Bob's if you want great BBQ. Their BBQ is just OK. I guess it would be good to go there just to say you've been there. If you do go, I'd recommend the chicken and with the white sauce. Also, try their pies, they are very good.
Enjoy your stay in Huntsville!