Arthur Bryants is in KC, have eaten there many a time, and Like Porkaholic said it is a vinegar based sauce, I like vinegar based sauces so it is one of my favorites, like said before try it out on a few different types of meat.
To me it is unlike any other sauce I have tried, a bit different, and I could see where some may say it's a bit gritty, definately a stronger vinegar taste, all i can say is try it out, let us know what ya think.
Lvrgsp