This study aimed to nutritionally and technologically characterize the meat produced by rabbit (Oryctolagus cuniculus, Flemish Giant breed, 50 farmed individuals) and hare (Lepus europaeus Pallas, 50 hunted individuals). Muscles were sampled from several carcass regions: dorsal torso—Longissimus dorsi (LD), thigh—Semimembranosus (SM), and upper arm—Triceps brachii (TB). To better depict the meat’s nutritional quality, the proximate composition and fatty acid profile were assessed, and then gross energy content and lipid sanogenic indices (Polyunsaturation—PI, atherogenic—AI, thrombogenic—TI, hypocholersyerolemic/hypercholesterolemic ratio—h/H, Nutritional Value Index—NVI) were calculated. pH values at 24 and 48 h post-slaughter, cooking loss (CL), and water-holding capacity (WHC) were the investigated technological quality traits. Gross energy was higher in rabbit TB samples, compared with hare, due to more accumulated lipids (p < 0.001). pH value was higher for TB muscles in both species; the WHC was higher for hare (p < 0.001), and CL was higher for rabbit (p < 0.001). The PI values were 6.72 in hare and 4.59 in rabbit, AI reached 0.78 in hare and 0.73 in rabbit, TI was calculated at 0.66 in hare and 0.39 in rabbit, and the h/H ratio reached 3.57 in hare and 1.97 in rabbit, while the NVI was 1.48 in hare and 1.34 in rabbit samples. Meat from both species is nutritionally valuable for human consumers, meeting nutritional values better than the meat of farmed or other wild species of fowl and mammals. Hare meat was found to be healthier than rabbit in terms of lower fat content, lighter energy, and better lipid health indices.