The relative rates of B-meson decays into J/psi and psi(2S) mesons are measured for the three decay modes in pp collisions recorded with the LHCb detector. The ratios of branching fractions (B) are measured to be B(B+ -> psi(2S)K+)/B(B+ -> J/psi K+) = 0.594 +/- 0.006(stat) +/- 0.016(syst) +/- 0.015(R-psi), B(B-0 -> psi(2S)K*(0))/B(B-0 -> J/psi K*(0)) = 0.476 +/- 0.014(stat) +/- 0.010(syst) +/- 0.012(R-psi), B(B-s(0) -> psi(2S)phi)/B(B-s(0) -> J/psi phi) = 0.489 +/- 0.026(stat) +/- 0.021(syst) +/- 0.012(R-psi), where the third uncertainty is from the ratio of the psi(2S) and J/psi branching fractions to mu(+)mu(-).