Phase velocities derived from ambient-noise cross-correlation are compared with phase velocities calculated from cross-correlations of waveform recordings of teleseismic earthquakes whose epicentres are approximately on the station–station great circle. The comparison is conducted both for Rayleigh and Love waves using over 1000 station pairs in central Europe. We describe in detail our signal-processing method which allows for automated processing of large amounts of data. Ambient-noise data are collected in the 5–80 s period range, whereas teleseismic data are available between about 8 and 250 s, resulting in a broad common period range between 8 and 80 s. At intermediate periods around 30 s and for shorter interstation distances, phase velocities measured from ambient noise are on average between 0.5 per cent and 1.5 per cent lower than those observed via the earthquake-based method. This discrepancy is small compared to typical phase-velocity heterogeneities (10 per cent peak-to-peak or more) observed in this period range.We nevertheless conduct a suite of synthetic tests to evaluate whether known biases in ambient-noise cross-correlation measurements could account for this discrepancy; we specifically evaluate the effects of heterogeneities in source distribution, of azimuthal anisotropy in surface-wave velocity and of the presence of near-field, rather than far-field only, sources of seismic noise. We find that these effects can be quite important comparing individual station pairs. The systematic discrepancy is presumably due to a combination of factors, related to differences in sensitivity of earthquake versus noise data to lateral heterogeneity. The data sets from both methods are used to create some preliminary tomographic maps that are characterized by velocity heterogeneities of similar amplitude and pattern, confirming the overall agreement between the two measurement methods.