We carry out numerical simulations with 3D self-propelled virtual swimmers, a mackerel (M) and an eel (E), to elucidate the role of form (body shape) and kinematics carangiform (C) vs. anguilliform (A) on the hydrodynamics of undulatory swimming. The motion of the fish mean line is prescribed but the forward swimming speed is calculated via the fluid-structure interaction (FSI) numerical approach of Borazjani et al [J. Comp. Physics, 227(16), 2008]. We consider: 1) a mackerel swimming as mackerel do in nature (M-C); 2) a mackerel swimming with anguilliform kinematics (M-A); 3) an eel swimming as eels do (E-A); and 4) an eel swimming with carangiform kinematics (E-C). Virtual swimmers with the same body shape race each other with different kinematics (M-C vs. M-A and E-C vs. E-A) in the same fluid (fixed viscosity) and with the same tail beat frequency. Regardless of body shape, anguilliform kinematics win the race in the transitional regime (Re = 4000) while carangiform kinematics prevail in the inertial regime (Inviscid limit). Our results support the notion that hydrodynamic considerations have played a role in the evolution of fish shapes and kinematics since in nature anguilliform kinematics are preferred in the transitional regime while carangiform kinematics are preferred in the inertial regime. Out results also show that the 3D structure of fish wakes (single vs. double row vortices) is largely independent of body shape and kinematics and support our previous findings [J. Exp. Biol. 211(10) 2008] that the Strouhal number is the key governing parameter.