This paper deals with the response of swirling flames submitted to acoustic velocity disturbances when the rotation of the flow is produced by an axial or a radial swirler. The objective is to compare responses obtained in these two cases. The response is characterized in terms of the flame describing function (FDF), which generalizes the classical flame transfer function concept by considering not only the frequency but also the amplitude of the velocity disturbances. Results indicate that for both types of swirlers, the dynamics is essentially similar for the gains and the phases of the FDF. It is also found that the swirl number value markedly influences the gain response. The characteristic shape of the FDF, with a local minimum and maximum, are found in both cases and these features correspond to mechanisms already described previously: swirl number fluctuations and vortex rollup of the flame. Swirl number fluctuations are induced by the interaction of the incident acoustic disturbances with the swirler. This generates in the two cases a transmitted acoustic wave and a convective vorticity wave. This last wave is characterized by azimuthal velocity perturbations. The mode conversion process giving rise to the latter type of disturbance was already demonstrated in the case of an axial swirler. It is here examined in the radial swirler geometry. It is shown that the mode conversion processes in the two geometries are quite similar and that they produce similar effects on the flame dynamics and response.