The difference in the density of states for up-and down-spin electrons in a ferromagnet (F) results in spin-dependent scattering of electrons at a ferromagnet / nonmagnetic (F/N) interface. In a F/N/F spin-valve, this causes a current-independent difference in resistance (∆R) between antiparallel (AP) and parallel (P) magnetization states. Giant magnetoresistance (GMR), ∆R = R(AP ) − R(P ), is positive due to increased scattering of majority and minority spin-electrons in the AP-state. If N is substituted for a superconductor (S), there exists a competition between GMR and the superconductor proximity effect: in the AP-state the net magnetic exchange field acting on S is lowered and the superconductivity is reinforced meaning R(AP ) decreases. For currentperpendicular-to-plane (CPP) spin-valves, existing experimental studies show that GMR dominates (∆R > 0) over the superconductor proximity effect (∆R < 0) [J. Y. Gu et al., Phys. Rev. B 66, 140507 (2002)]. Here, however, we report a crossover from GMR (∆R > 0) to the superconductor proximity effect (∆R < 0) in CPP F/S/F spin-valves as the superconductor thickness decreases below a critical value. The results are key to the development of quasiparticle spintronics.