In order to verify the channel sum-rate improvement by multi-user multiple-input multiple-output (MU-MIMO) transmission in distributed antenna systems (DASs), we investigate and compare the characteristics of channel sum-rates in both centralized antenna systems (CASs) and DASs under the effects of path loss, spatially correlated shadowing, correlated multi-path fading, and inter-cell interference. In this paper, we introduce two different types of functions to model the shadowing, auto-correlation and cross-correlation, and a typical exponential decay function to model the multi-path fading correlation. Thus, we obtain the distribution of the channel sum-rate and investigate its characteristics. Computer simulation results indicate that DAS can improve the performance of the channel sum-rate compared to CAS, even in the case under consideration. However, this improvement decreases as interference power increases. Moreover, the decrease in the channel sum-rate due to the increase in the interference power becomes slow under the effect of shadowing correlation. In addition, some other analyses on the shadowing correlation that occurs on both the transmit and receiver sides are provided. These analysis results show that the average channel sum-rate in a DAS without inter-cell interference considerably decreases because of the shadowing correlation. In contrast, there appears to be no change in the CAS. Furthermore, there are two different types of sum-rate changes in a DAS because of the difference in shadowing auto-correlation and cross-correlation.