We show, for the first time, radio measurements of the depth of shower maximum (X_{max}) of air showers induced by cosmic rays that are compared to measurements of the established fluorescence method at the same location. Using measurements at the Pierre Auger Observatory we show full compatibility between our radio and the previously published fluorescence dataset, and between a subset of air showers observed simultaneously with both radio and fluorescence techniques, a measurement setup unique to the Pierre Auger Observatory. Furthermore, we show radio X_{max} resolution as a function of energy and demonstrate the ability to make competitive high-resolution X_{max} measurements with even a sparse radio array. With this, we show that the radio technique is capable of cosmic-ray mass composition studies, both at Auger and at other experiments.