The performance of multiple input multiple output (MIMO) systems is greatly influenced by the spatial correlation properties of the underlying MIMO channels. This paper investigates the spatial correlation characteristics of the Spatial Channel Model (SCM) in the Third Generation Partnership Project (3GPP) and the Kronecker Based Stochastic Model (KBSM) at three levels, namely the cluster level, link level, and system level. The KBSM has the spatial separability at all the three levels. The SCM shows the spatial separability at the link and system levels, but not at the cluster level since its spatial correlation is related to the joint distribution of the angle of arrival (AoA) and angle of departure (AoD). The KBSM with the Gaussian shaped Power Azimuth Spectrum (PAS) is found to fit best the 3GPP SCM in terms of the spatial correlations. Despite of its simplicity and analytical tractability, the KBSM is restricted to model only the average spatial behavior of MIMO channels. The SCM provides more insights of the variations of different MIMO channel realizations but the implementation complexity is relatively high.