We want to characterize the dynamical state of galaxy clusters detected with the Sunyaev–Zeldovich (SZ) effect by Planck and compare them with the dynamical state of clusters selected in X-rays survey. We analysed a representative subsample of the Planck SZ catalogue, containing the 132 clusters with the highest signal to noise ratio and characterize their dynamical state using as an indicator the projected offset between the peak of the X-ray emission and the position of the Brightest cluster galaxy. We compare the distribution of this indicator for the Planck SZ-selected sample and three X-ray-selected samples (HIFLUGCS, MACS and REXCESS). The distributions are significantly different and the fraction of relaxed objects is smaller in the Planck sample (52 ± 4 per cent) than in X-ray samples (≃74 per cent) We interpret this result as an indication of different selection effects affecting X-rays (e.g. ‘cool core bias’) and SZ surveys of galaxy clusters.