Wash fresh peaches, if using. Peel and pit peaches. Place half of the fresh or frozen peaches in a food processor bowl or blender container. Cover and process or blend until peaches are very finely chopped. Transfer chopped peaches to a 6-quart Dutch oven or kettle. Repeat with remaining peaches. (You should have 5 cups pureed peaches.)
Add sugar, nectar, vinegar, lemon juice, garlic, chili pepper, and 1/2 teaspoon salt to Dutch oven. Bring to boiling; reduce heat. Simmer, uncovered, 15 to 20 minutes or until desired consistency, stirring occasionally. Remove from heat. Stir in berries.
Process sauce in standard canning jars following directions below, or ladle into decorative jars and store in the refrigerator for up to 1 week before using.
To process the sauce, immediately ladle hot sauce into hot, clean half-pint canning jars, leaving 1/4-inch headspace. Wipe rims and adjust lids. Process jars in a boiling water canner 15 minutes (start timing when water begins to boil). Remove jars from canner; cook on racks. Stir sauce before serving. Makes 8 half-pint jars.