In a straight-sided skillet, heat 2-inches of oil, over medium-high heat. Oil is ready when the tip of a wooden skewer is inserted and the oil bubbles around it. When oil is ready, carefully fry ravioli until golden brown, about 1 minute per side. Drain on a paper towel-lined plate.
For Tomato Pepper Relish: In small bowl, combine red peppers and tomatoes. Stir in brown sugar and balsamic vinegar; set aside.
For Artichoke Caper Dip: In small bowl, combine artichoke hearts, capers, mayonnaise, sour cream, parmesan cheese, and lemon juice; set aside.
Serve ravioli hot with Tomato Pepper Relish and Artichoke Caper Dip.