Generally speaking....KC BBQ smothers...and I mean smother their meat with a sweet bbq sauce. Also, meats used is beef and pork, pulled pork in particular. My first time having pulled pork was in Nashville years ago for a friends wedding, her parents made a big deal that they were throwing a big bbq for everyone from Texas, we all looked at it....hesitated...politely made our plates and nibbled on it! The meat wasn't bad, pretty bland but the sauce was god awful..super sweet.
Texas BBQ...anything and everything that moves can be "BBQ"! The main meats would be Chicken, Brisket, Sausage, and Turkey and within the last 5-10 years we've seen more of the pulled pork type offerings....though most "good bbq joints" do not serve pulled pork. We use lots of dry rubs to flavor the meats as well as smoking it with mesquite, pecan, cherry, etc...instead of grilling, there are acceptable ways to grill some food such as sausage links, shrimp, fish etc, just throw some good mesquite or your favorite rub on it and cook!
Sauces are there for accents but not intended to smother it. Most sauces are tomato based (not vinegar) as well as having garlic and other spices and can "stay with you" for a couple of hours after eating...burp and you get the joy or re-tasting the sauce!!
One of the sauces I use is the standard sauce from Goode Co, a Houston institution as well as their Mesquite rub is outstanding too
Another Mesquite option is from Fiesta that you can find at most grocery stores.
Again...Im speaking in general terms.