An unbreakable relationship between plants, nutrition, and health has directed researchers to deeply investigate and characterize the biopotential and medicinal properties of traditional foods. The aim of this study is to analyze and compare the phytochemical composition and biological potential of plant extracts with the idea of defining the most potent extracts as a natural source of bioactive molecules and their application in different industries. We evaluated unused plant species Sambucus nigra L. for investigation of bioactivities as potential natural products. Extracts of fresh elderberry fruits were obtained by modern (microwave-assisted extraction (MAE), ultrasound-assisted extraction (UAE)) and traditional (maceration (MAC)) extraction techniques, using 50% ethanol (50% EtOH) and water (H2O) of different polarities. In analyzed extracts, rutin and chlorogenic acid were dominant compounds in both 50% EtOH and H2O extracts, while ursolic acid was identified in 50% EtOH extracts as a terpenic compound with notable concentration. Elderberry extracts were evaluated regarding antioxidant, neuroprotective, antityrosinase, and antidiabetic abilities: MAE extracts had the best overall activity, and in general, 50% EtOH extracts were more potent than water extracts. The correlation of the dominant compound—rutin with all biological activities, indicates the importance of its presence in elderberries. S. nigra fruits showed excellent biopotential and opened possibilities of creating new food products or remedies, which are not present on the market because elderberry extracts are an exceptional source of rutin, chlorogenic acid, and ursolic acid.