A friend of mine lives in LR so I solicited his opinions:
"BBQ. So subjective on what people like. I'm a fan of Whole Hog pulled pork in North Little Rock. There's more than one. If they want ribs I send them to the Whole Hog in Little Rock. Avoid Corkey's like the plague. There's also Sim's and HB's but they're more of a local tradition than anything outstanding from the flavor side of things. Both are in rough parts of town as well. Chicken is still good at the Capitol Smokehouse downtown. They changed owners and the pork went to hell."
Hope this helps!