Toss chickpeas, tomatoes, feta cheese, and basil together in a large mixing bowl.
Put honey in a small glass bowl; heat in microwave 30 seconds. Stir garlic, red wine vinegar, cider vinegar, olive oil, black pepper, cayenne pepper, and salt with the honey to make a dressing; pour over the chickpea salad and toss to coat.
Cover the mixing bowl with plastic wrap. Refrigerate salad for 1 hour before serving.
