The aim of this study was to represent quality characterization, by gender and muscle type, of rabbit meat from the Flemish Giant (FG) breed, following the fatty acid profile, sanogenic indices, and instrumental (color and texture) and sensory analysis. The biological material comprised 40 rabbits (20 females and 20 males) whose Longissimus dorsi (LD) and Semimembranosus (SM) muscles were sampled. Compared to female samples, the meat from males was more qualitative in terms of higher ratios of polyunsaturated vs. saturated fatty acids and proportions (+42%) of Essential and Desirable Fatty Acids (+21.6% EFA; +6.7% DFA). Also, the Atherogenic Index (AI) and Thrombogenic Index (TI) were better in males (−37.1% AI; −34.3% TI), as were the ratio of hypocholesterolemic/Hypercholesterolemic fatty acids (+27.8%) and the Nutritive Value Index (NVI, +11.6%). The Polyunsaturation Index (PI) was higher for females (+57.5%), with the widest differences in hind leg muscles (SM muscles), while the omega-6/omega-3 fatty acid ratio was also better (+11.3%). Female meat was more tender due to lower shear force (−6.2%… 9.3%) in both muscles. Female meat was less pigmented than that of males, while the overall sensory attributes were better scored in male samples (+3.1%… +7.1%) (p < 0.01). The meat of males proved to be more sanogenic (richer in EFA and DFA, with a better h/H ratio and NVI, while AI and TI were lower). We would recommend slaughtering 3–4 weeks earlier in females vs. males to avoid excessive fat deposition and, consequently, the development of unfavorable sanogenic indices for consumer health.