Charge exchange is examined with unprecedented precision using the newly developed magneto-optical trap-target recoil ion momentum spectroscopy (MOTRIMS) technique. Initial and final state selective, charge exchange cross sections are obtained for 6 keV Cs+ colliding with rubidium in 5s and 5p states. For each charge transfer channel, cross sections differential in scattering angle are measured. These data are used to overturn previous long-standing conjecture as to the origin of oscillations seen in total charge exchange cross section measurements, and compare well with an enhanced Demkov model calculation.