The present work tackles the question on the evidence of X-ray phase contrast imaging with regard to a potential application in medical diagnostics. For this study the Talbot-Lau interferometer method by means of X-ray diffraction gratings was used. Specimens of human organs (e.g., adrenal gland, liver, blood vessels, etc.) were prepared and tomographic measurements were performed. The grating interferometer was developed and optimized for higher fractional Talbot orders, i.e., n = 12, in order to improve the phase sensitivity of the system. The measurements with the grating interferometer simultaneously deliver two independent projection image data sets, one reflects the X-ray attenuation coefficient, equivalent to radiography or CT, and the second one uses the refraction index, which corresponds to the phase contrast. Both data sets were reconstructed which allows for the direct comparison of the two contrast mechanisms. It was shown that the achieved phase sensitivity is sufficient to reveal anatomical details and morphology in soft tissue. Moreover, it was shown that the two contrast mechanisms can deliver complementary information. For instance, specific features, such as blood vessels, are rendered more distinct by the phase contrast images than by the attenuation images.