The relative rates of B-meson decays into J/ψ and ψ(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+ → ψ(2S)K+) B(B+ → J/ψK+) = 0.594 ± 0.006(stat) ± 0.016(syst) ± 0.015(Rψ ), B(B0 → ψ(2S)K∗0) B(B0 → J/ψK∗0) = 0.476 ± 0.014(stat) ± 0.010(syst) ± 0.012(Rψ ), B(B0 s → ψ(2S)φ) B(B0 s → J/ψφ) = 0.489 ± 0.026(stat) ± 0.021(syst) ± 0.012(Rψ ), where the third uncertainty is from the ratio of the ψ(2S) and J/ψ branching fractions to μ+μ−.