The increasing popularity of pomegranate (Punica granatum L.), driven by the awareness of its nutraceutical properties and excellent environmental adaptability, is promoting a global expansion of its production area. This investigation reports the variability in the weight, moisture, pH, total soluble solids, carbohydrates, organic acids, phenolic compounds, fatty acids, antioxidant activities, and element composition of different fruit parts (juices, peels, and kernels) from four (Ako, Emek, Kamel, and Wonderful One) of the most widely cultivated Israeli pomegranate varieties in Salento (South Italy). To the best of our knowledge, this is the first systematic characterization of different fruit parts from pomegranate cultivars grown simultaneously in the same orchard and subjected to identical agronomic and environmental conditions. Significant genotype-dependent variability was observed for many of the investigated parameters, though without any correlation among fruit parts. The levels of phenols, flavonoids, anthocyanins, and ascorbic and dehydroascorbic acids of all samples were higher than the literature-reported data, as was the antioxidant activity. This is likely due to positive interactions among genotypes, the environment, and good agricultural practices. This study also confirms that pomegranate kernels and peels are, respectively, rich sources of punicic acid and phenols together, with several other bioactive molecules. However, the variability in their levels emphasizes the need for further research to better exploit their agro-industrial potential and thereby increase juice-production chain sustainability. This study will help to assist breeders and growers to respond to consumer and industrial preferences and encourage the development of biorefinery strategies for the utilization of pomegranate by-products as nutraceuticals or value-added ingredients for custom-tailored supplemented foods.