If using a gas grill, preheat to high on one side; put soaked wood chips in a smoker box. Once smoking, reduce the heat to maintain a temperature of 275 degrees F and cook the pork, covered, on the cooler side of the grill.
Mix the paprika, sugar and onion powder in a bowl. Add 2 tablespoons salt and 3 tablespoons pepper, and massage onto the pork. Cover with plastic wrap and refrigerate at least 2 hours or up to 1 day.
Soak 6 cups wood chips in water, about 15 minutes, then drain. Don't soak long or the wood will snuff out the fire.
Fill a smoker or kettle grill with charcoal and light. When the coals are mostly white, spread them out with tongs. Spread 1/2 cup of the wood chips over the coals (use 1 cup for a kettle grill). The temperature of the grill should be about 275 degrees F.
Place the pork fat-side down on a rack in the smoker or on the grill. Cover and cook, rotating the pork every hour or so, until a thermometer inserted into the center registers 165 degrees F, about 6 hours total.
As the pork cooks, add more charcoal and wood chips to keep the temperature between 250 degrees F and 275 degrees F and to maintain the smoke level.
Transfer the pork to a rimmed baking sheet (you'll want to catch all the flavorful juices) and let stand until cool enough to handle. Shred into bite-size pieces, pile on a platter and pour any juices from the baking sheet over the meat.
Serve on a bun with coleslaw and barbecue sauce, or pickles and mustard.