The aims of the present study were to analyze mobility, dynamic balance and lower-limb strength and the prevalence of asymmetry according to the type of sport and assess the association between inter-limb asymmetry and sports performance. A total of 23 basketball and 25 handball players performed a test battery consisting of functional movements and a jump test. Inter-limb asymmetry was calculated using a standard percentage difference equation. A between-groups comparison analysis was carried out, and Pearson’s correlation coefficients (r) were calculated to establish a relationship between asymmetries and physical performance. The results found athletes in different sports to exhibit different performance in functional movements and the jump test, but no bilateral asymmetries. The reactive strength index (RSI) and stiffness asymmetries were significantly associated with the anterior reach Y-balance test (YBT) (r = −0.412; p < 0.01 and r = −0.359; p < 0.05, respectively), and the unilateral triple hop test (THTU) was negatively correlated to anterior reach, posterior lateral reach YBT and YBT composite YBT (r = −0.341 to −0.377; p < 0.05). These findings suggest that the asymmetries exhibited important dispersion not dependent upon the type of sport but on each individual and the applied test. In addition, asymmetry in anterior direction YBT showed the strongest association to the rest of the sports performance variables.