We consider an XXZ spin-1/2 chain coupled to optical phonons with nonzero frequency ω0. In the adiabatic limit (small ω0), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become static. In the antiadiabatic limit (large ω0), phonons are expected to give rise to frustration, so that dimerization and formation of spin gap are obtained only when the spin-phonon interaction is large enough. We study this crossover using bosonization technique. The effective action is solved both by the self-consistent harmonic approximation (SCHA) and by renormalization group (RG) approach starting from a bosonized description. The SCHA allows to analyze the low-frequency regime and determine the coupling constant associated with the spin-Peierls transition. However, it fails to describe the SU(2) invariant limit. This limit is tackled by the RG. Three regimes are found. For ω0⪡Δs, where Δs is the gap in the static limit ω0→0, the system is in the adiabatic regime, and the gap remains of order Δs. For ω0>Δs, the system enters the antiadiabatic regime, and the gap decreases rapidly as ω0 increases. Finally, for ω0>ωBKT, where ωBKT is an increasing function of the spin-phonon coupling, the spin gap vanishes via a Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in relation with numerical and experimental studies of spin-Peierls systems.