In this paper, six recently proposed massive multiple-input multiple-output (MIMO) channel models are described briefly, and their normalized channel capacities and spatial cross-correlation functions (CCFs) are further compared. Among these models, two dimensional (2D) elliptical model, 2D parabolic model, three dimensional (3D) twin-cluster model, 3D 5G channel model, and 3D ellipsoid model are geometry-based stochastic models (GBSMs), while 2D Kronecker-based stochastic model with birth-death (BD) process on the array axis (KBSM-BD-AA) is a correlation-based stochastic model (CBSM). The 3D channel characteristics considering the elevation angles of massive MIMO channels, and 2D channel characteristics are investigated. The simulation results show that the spatial CCFs and channel capacities of 3D channel models are larger than those of the corresponding 2D channel models.