In this paper we describe a method for quantitative photoacoustic tomography (qPAT) based on the photon radiative transfer equation (RTE) coupled with the Helmholtz photoacoustic wave equation. Considerable simulations and tissue-like phantom experiments are conducted to evaluate transport-based qPAT in comparison with diffusion-based qPAT. In these comparative simulations and experiments, we systematically examine the effects of the ratio of μa/μ's (absorption/reduced scattering coefficient), the anisotropy factor (g) and the imaging domain size on the transport- and diffusion-based photoacoustic image reconstruction. The results obtained show that transport-based qPAT allows for clearly more accurate recovery of the absolute absorption coefficient images of heterogeneous media over diffusion-based qPAT for all the cases examined and provides considerably improved image quality for cases where the photon diffusion approximation (DA) is invalid.