I also live in the KC area and haven't been to too many of the BBQ restaurants, but I'll post what I know.
Jack Stack - I like Jack Stack. It is definitely a nicer restaurant setting and NOT a hole in the wall type place. The normal stuff (pulled pork, pork ribs, brisket, etc.) is OK, but the prime beef ribs, the lamb ribs, and their beans are really good. They have the best beans I've ever had.
Q39 - My family loves Q39. The brisket is the best I've had at a restaurant. They also have great burnt ends. I've never had a meal there I didn't love. It is like Jack Stack in that it is also a nicer restaurant setting and NOT a hole in the wall type place.
Arthur Bryant's - This has been my least favorite place. I didn't go to the main/original location, and I've heard that better, but my experience was not great.
Gates - I've been to Gates a few times. I like it. It's OK/good. It is more of a run down and informal type setting. You need to know what you want when you get to the counter to order though
My family does not love it, and we probably won't go back because of that. I really like their BBQ sauce. Their spicy sauce is good.
Smoking Guns - I thought it was OK. Nothing special when I went. My dad really liked it though...
Joe's Kansas City - I love Joe's. Their burnt ends rival Q39's and are really good, but I think they only sell burnt ends a couple days a week. The Z-man sandwich is great. It has sliced brisket, some BBQ sauce, smoked provolone, and onion rings. Good stuff. If you go to the original location it is in an old gas station, so if you're not looking for a restaurant type setting that is a good option, but there will be some wait/lines usually.
Plowboys - This place is close by where I live and, like many people, I have been using their rubs for a while. I thought it was pretty good. I liked their ribs a lot and their BBQ nachos are pretty good.
That's all I can think of at the moment, but I think I've been to a few others...
Enjoy!