Context. Photoevaporation and magnetically driven winds are two independent mechanisms that remove mass from protoplanetary disks. In addition to accretion, the effect of these two principles acting concurrently could be significant, and the transition between them has not yet been extensively studied and quantified. Aims. In order to contribute to the understanding of disk winds, we present the phenomena emerging in the framework of two-dimensional axisymmetric, nonideal magnetohydrodynamic simulations including extreme-ultraviolet (EUV) and X-ray driven photoevaporation. Of particular interest are the examination of the transition region between photoevaporation and magnetically driven wind, the possibility of emerging magnetocentrifugal wind effects, and the morphology of the wind itself, which depends on the strength of the magnetic field. Methods. We used the PLUTO code in a two-dimensional axisymmetric configuration with additional treatment of EUV and X-ray heating and dynamic ohmic diffusion based on a semi-analytical chemical model. Results. We determine that the transition between the two outflow types occurs for values of the initial plasma beta β ≥ 10⁷, while magnetically driven winds generally outperform photoevaporation for stronger fields. In our simulations we observe irregular and asymmetric outflows for stronger magnetic fields. In the weak-field regime, the photoevaporation rates are slightly lowered by perturbations of the gas density in the inner regions of the disk. Overall, our results predict a wind with a lever arm smaller than 1.5, consistent with a hot magnetothermal wind. Stronger accretion flows are present for values of β < 10⁷.