Among the X-ray phase contrast imaging (XPCI) techniques, both propagation-based and grating-based micro-tomography recently dominate the non-destructive three-dimensional inner-structure measurement in biomedical research, especially for visualizing tiny density variations in soft tissues and organs. In order to quantitatively evaluate the advantages and disadvantages of both techniques for comprehensive application through carrying out a comparison study of high energy propagation-based micro-tomography with generalized phase-and-attenuation duality (PAD) phase retrieval and Talbot grating interferometer-based micro-tomography, implemented with two biomedical specimens, mouse fetus and rat brain, on the basis of synchrotron radiation facility. We find that the grating-based micro-tomography is superior in the contrast-to-noise ratio (CNR) or the mass density resolution, and inferior in the spatial resolution (SR), compared with that of propagation-based micro-tomography. We found that for achieving a given CNR, the grating-based micro-tomography applies about 1.5 times radiation dose involved as compared to the propagation-based micro-tomography with PAD phase retrieval. Additionally, the complex coherent degrees of light source related to the both techniques were duly taken into account in the analysis of their SR comparison. Finally, the mass density distribution of soft biomedical specimens can be estimated using our presented method preliminarily. Our work gives indications for applications and developments of phase sensitive micro-tomography for soft biomedical specimens and low-Z materials.