Once you are done with pulled pork recipe, place it directly on the grill grates of the smoker (fatty side up is best). Close the lid and smoke for 15-20 hours, or until the internal temperature of the pork reaches 195-201 degrees F. Rest, slice and serve. Pulled pork is grilled easily as compared to grilling beef brisket. Beef brisket vs pulled pork can be grilled.