Pilot contamination is known to be one of the main bottlenecks for massive multi-input multi-output (MIMO) networks. For moderately large antenna arrays (of importance to recent/emerging deployments) and correlated MIMO, pilot contamination may not be the dominant limiting factor in certain scenarios. To the best of our knowledge, a rigorous characterization of the achievable rates and their explicit dependence on the angular spread (AS) is not available in the existing literature for moderately large antenna array regime. In this paper, considering eigen-beamforming (EBF) precoding, we derive an exact analytical expression for achievable rates in multi-cell MIMO systems under pilot contamination, and characterize the relation between the AS, array size, and respective user rates. Our analytical and simulation results reveal that the achievable rates for both the EBF and the regularized zero-forcing (RZF) precoders follow a non-monotonic behavior for increasing AS when the antenna array size is moderate. We argue that knowledge of this non-monotonic behavior can be exploited to develop effective user-cell pairing techniques.