We carry out a study of the global three-dimensional (3D) structure of the electron density and temperature of the quiescent inner solar corona ( r < 1.25 R ⊙ ) by means of tomographic reconstructions and magnetohydrodynamic simulations. We use differential emission measure tomography (DEMT) and the Alfvén Wave Solar Model (AWSoM), in their latest versions. Two target rotations were selected from the solar minimum between Solar Cycles (SCs) 23 and 24 and the declining phase of SC 24. We report in quantitative detail on the 3D thermodynamic structure of the core and outer layers of the streamer belt, and of the high latitude coronal holes (CH), as revealed by the DEMT analysis. We report on the presence of two types of structures within the streamer belt, loops with temperature decreasing/increasing with height (dubbed down/up loops), as reported first in previous DEMT studies. We also estimate the heating energy flux required at the coronal base to keep these structures stable, found to be of order 10 5 erg cm − 2 s − 1 , consistently with previous DEMT and spectroscopic studies. We discuss how these findings are consistent with coronal dissipation of Alfvén waves. We compare the 3D results of DEMT and AWSoM in distinct magnetic structures. We show that the agreement between the products of both techniques is the best so far, with an overall agreement ≲ 20 % , depending on the target rotation and the specific coronal region. In its current implementation the ASWsoM model cannot reproduce down loops though. Also, in the source region of the fast and slow components of the solar wind, the electron density of the AWSoM model increases with latitude, opposite to the trend observed in DEMT reconstructions.