Hard X-ray nanotomography is a promising technology for nondestructive imaging of biological tissues with three-dimensional isotropic resolution. The implementation of fourth-generation synchrotron sources brings coherent X-ray microscopy to the central stage and fosters further development of this class of techniques. Here, we present an experimental comparison of X-ray near-field ptychography and X-ray holography, two high-resolution X-ray microscopy techniques applied under cryogenic conditions to the exact same sample at two different synchrotron sources. Using a heavy-metal-stained, resin-embedded brain tissue sample, we obtain similar contrast and spatial resolutions at equivalent radiation doses with these two approaches. We discuss the current benefits and limitations of the two methods. These results provide a basis for developments in X-ray microscopy of biological samples at present and future beamlines of fourth-generation synchrotron sources.