In medical imaging systems, proper rendition of anatomy is essential in discerning normal tissue from disease. Currently, digital breast tomosynthesis (DBT) systems are evaluated using subjective evaluation of lesion visibility in uniform phantoms. This study involved the development of a new methodology to objectively measure the rendition of a 3D breast model by an anthropomorphic breast phantom, and its implementation on five clinical DBT systems of different makes and models. A 3D, patient-based breast phantom was fabricated based on XCAT breast models. This phantom was imaged on representative breast tomosynthesis systems. The ability of tomosynthesis systems to accurately reproduce the 3D structure of the breast was assessed by computational analysis of the resultant images in terms of three groups of indices: contrast index (CI), reflective of local difference between adipose and glandular material; adipose variability index (AVI), reflective of contributions of noise and artifacts within uniform adipose regions; and contrast detectability, which describes contrast against local background variability and is described by contrast variability index (CVI), coefficient of variation (COV), contrast to adipose variability index (CAVI), and contrast to noise ratio index (CNRI). The indices were obtained by comparing the image data to the gold standard 3D distribution of breast tissue in the model. Corresponding indices were measured within variable region of interest (ROI) sizes ranging from 10 to 37 mm. The characterization was performed on five tomosynthesis systems: Fuji Aspire Crystal, GE Essential, Hologic Dimension, IMS Giotto, and Siemens Inspiration, all evaluated at a fixed dose of 1.5 mGy average glandular dose, anonymized in random order from A to E. Results are provided as a function of ROI size. The systems ranked orders in terms of CI with values of 7.4%, 7.0%, 6.9%, 6.4%, and 5.2% for systems A-E, respectively. This system ranking was identical for CNRI. Both CI and CNRI were constant over ROI size. The ranking was similar for CVI. The COV also changed little with ROI size and was similar across systems. For 10 mm ROIs, the average system COV was 0.7, which reduced to 0.5 with 37 mm ROIs. Two systems (A and B) exhibited highest AVI values when measured in 10 mm ROIs. This, however, was ROI-size-dependent with the three other systems (C-E) yielding higher AVI values when measured with 37 mm ROIs. Two systems (B and E) showed inferior CAVI compared to others. The quality of rendition tracked with differences in image appearance across systems. The findings illustrate that the anthropomorphic phantom can be used as a basis to extract quantitative values of image attributes in DBT.