Pull the meat from the chickens, discarding skin (if desired) and bones. Using two forks or your fingers, pull the meat into shreds. If desired, chop the seasoned skin and add it to the chicken.
In a 4-quart Dutch oven, heat the olive oil over medium heat. Add onion and sweet pepper; cook and stir about 5 minutes or until tender. Add vinegar. Cook and stir for 1 minute more. Stir in tomato sauce, basil, honey, and salt. Bring to boiling. Add the chicken, tossing gently to coat. Heat through.
To serve, use a slotted spoon to place chicken mixture on bottoms of bread loaves. Top with pickle slices; replace tops of bread. Cut loaves into serving-size portions. Makes 12 servings.