Tomato grafting is an effective practice in increasing the profitability of fresh-market tomato cultivation, especially in greenhouses, and is also considered a strategy for enhancing fruit quality. In this study, selected quanti-qualitative traits, and the of bioactive health-promoting compound and organic acid contents of cherry tomato fruits from three different scion/rootstock combinations (Sunstream/Top Bental, Sunstream/Kaiser and Sunstream/Suzuka) grown under a greenhouse hydroponic system were evaluated in three different harvests (beginning, middle and end of the whole harvesting period) and on three different bunch portions (proximal, central and distal). Although the tomato productive performance was influenced by the rootstock, with Suzuka and Kaiser grafted plants showing the highest total marketable yield (9.8 kg plant−1, i.e., 20% more than Top Bental), the yield-related traits (bunch number, weight and length per plant, and fruit number per bunch) and the qualitative characteristics of the fruits (color, equatorial and polar diameters, dry matter and solid soluble contents, pH and titratable acidity) showed less variability, by displaying, along with the bioactive compound contents (total polyphenols, lycopene, β-carotene), DPPH free radical scavenging activity and organic acids contents (lactic and acetic), a significant effect of the harvesting time and bunch portion. Fruits from the beginning of the harvesting period showed better qualitative and functional properties, with the lycopene and β-carotene contents equal to 178.6 and 3 mg 100 g−1 fw, and fruits from proximal and central bunch portions had lycopene and β-carotene contents equal to 203.1 and 2.9 mg 100 g−1 fw.