The witnesses of the millenary history of Campania felix in southern Italy highlighted that several fruit and vegetables cultivated in such territory could potentially be a treasure trove of important health elements. Our work evaluated the content of β-carotene, ascorbic acid, and total phenolics and the antioxidant activity of ten typical varieties of apricots cultivated in the Vesuvius area in the Campania region. The total polyphenols varied between 10.24 and 34.04 mg/100 g of a fresh sample. The amount of ascorbic acid also varied greatly, ranging from 2.65 to 10.65 mg/100 g of a fresh product. B-Carotene reached values up to 0.522 mg/100 g of the fresh sample. The correlation analysis performed, accounting for these parameters, showed that the antioxidant activity, calculated by 2,2-diphenyl-1-picrylhydrazyl (DPPH assay) and azino-bis (3-ethylbenzothiazoline-6-sulfonic acid) tests, was influenced mainly by the content of total polyphenols, with ρ = −0.762 and ρ = 0.875 when we considered DPPH and ABTS tests, respectively, slightly less by the content of ascorbic acid, and not by β-carotene. The dendrogram clustered eight varieties into two main groups; on the other hand, two varieties (“Vitillo” and “Preveta bella”) seemed hierarchically distant. The gas chromatography–mass spectrometry (GC–MS) analysis of volatile organic compounds (VOCs), herein performed for the first time, demonstrated the influence of the varieties on the VOC profiles, both from a qualitative and semiquantitative perspective, discriminating the varieties in different clusters, each of which was characterized by specific notes. α-Terpinolene was the only terpene identified by GC–MS that appeared to affect the antioxidant activity.