In the present study, the extracts of Cytinus hypocistis (L.) L using both traditional solvents (hexane, ethyl acetate, dichloromethane, ethanol, ethanol/water, and water) and natural deep eutectic solvents (NADESs) were investigated in terms of their total polyphenolic contents and antioxidant and enzyme-inhibitive properties. The extracts were found to possess total phenolic and total flavonoid contents in the ranges of 26.47–186.13 mg GAE/g and 0.68–12.55 mg RE/g, respectively. Higher total phenolic contents were obtained for NADES extracts. Compositional differences were reported in relation to antioxidant potential studied by several assays (DPPH: 70.19–939.35 mg TE/g, ABTS: 172.56–4026.50 mg TE/g; CUPRAC: 97.41–1730.38 mg TE/g, FRAP: 84.11–1534.85 mg TE/g). Application of NADESs (choline chloride—urea 1:2, a so-called Reline) allowed one to obtain the highest number of extracts having antioxidant potential in the radical scavenging and reducing assays. NADES-B (protonated by HCl L-proline-xylitol 5:1) was the only extractant from the studied solvents that isolated a specific fraction without chelating activity. Reline extract exhibited the highest acetylcholinesterase inhibition compared to NADES-B and NADES-C (protonated by H2SO4 L-proline-xylitol 5:1) extracts, which showed no inhibition. The NADES extracts were observed to have higher tyrosinase inhibitory properties compared to extracts obtained by traditional organic solvents. Furthermore, the NADES extracts were relatively better inhibitors of the diabetic enzymes. These findings provided an interesting comparison in terms of total polyphenolic content yields, antioxidant and enzyme inhibitory properties (cholinesterase, amylase, glucosidase, and tyrosinase) between traditional solvent extracts and NADES extracts, used as an alternative. While the organic solvents showed better antioxidant activity, the NADES extracts were found to have some other improved properties, such as higher total phenolic content and enzyme-inhibiting properties, suggesting functional prospects for their use in phytonutrient extraction and fractionation. The obtained results could also be used to give a broad overview of the different biological potentials of C. hypocistis.