Optimal BeamFormers (BFs) that maximize the Weighted Sum Rate (WSR) for a Multiple-Input Multiple-Output (MIMO) interference broadcast channel (IBC) remains an important research area. Under practical scenarios, the problem is compounded by the fact that only partial channel state information at the transmitter (CSIT) is available. Hence, a typical choice of the optimization metric is the Expected Weighted Sum Rate (EWSR). However, the presence of the expectation operator makes the optimization a daunting task. On the other hand, for the particular, but significant, special case of massive MIMO (MaMIMO), the EWSR converges to Expected Signal covariance Expected Interference covariance based WSR (ESEI-WSR) and this metric is more amenable to optimization. Recently, [1] considered a multi-user Multiple-Input Single-Output (MISO) scenario and proposed approximating the EWSR by ESEI-WSR. They then derived a constant bound for this approximation. This paper performs a refined analysis of the gap between EWSR and ESEI-WSR criteria for finite antenna dimensions.