Inverse scattering is considered one of the most robust and accurate ultrasonic tomography methods. Most inverse scattering formulations neglect density changes in order to reconstruct sound speed and acoustic attenuation. Some studies available in literature suggest that density distributions can also be recovered using inverse scattering formulations. Two classes of algorithms have been identified. (1) The separation of sound speed and density contributions from reconstructions using constant density inverse scattering algorithms at multiple frequencies. (2) The inversion of the full wave equation including density changes. In this work, the performance of a representative algorithm for each class has been studied for the reconstruction of circular cylinders: the dual frequency distorted Born iterative method (DF-DBIM) and the T-matrix formulation. Root mean square error values lower than 30% were obtained with both algorithms when reconstructing cylinders up to eight wavelengths in diameter with moderate density changes. However, in order to provide accurate reconstructions the DF-DBIM and T-matrix method required very high signal-to-noise ratios and significantly large bandwidths, respectively. These limitations are discussed in the context of practical experimental implementations.