In small spaces in which typical cell towers cannot be constructed, distributed antenna systems (DASs) are the preferable approach for increasing network coverage, as they are a superior solution for congested, high-volume areas. However, due to their high cost and complexity in backhaul routing, reconfigurable intelligent surfaces (RISs) are a promising solution to overcome the major drawbacks of DAS systems while improving network coverage. Thus, this work investigated a correlation of execution in an RIS-aided system cell framework and DAS-aided system cell framework where a simple and precise structure for the performance measurement of area spectral efficiency (ASE) and energy efficiency (EE) under realistic channel presumptions was introduced. The analysis started with the downlink ergodic capacity with regards to the RIS framework and DAS framework under a generalized Nakagami-m fading channel with the presence of path-loss attenuation and interference from co-channel base stations (BSs), and was simplified further by utilizing a moment-generating function (MGF)-based approach. From the computed expression, the effects of traffic activity, EE and ASE were derived and analyzed for both systems in the presence of co-channel interference. The results were then verified by comparing them with Monte Carlo simulations, and the findings show that the two outcomes generally match. Based on these, it is demonstrated that the ASE performance of the RIS-assisted system in various traffic activity conditions outperforms the DAS-aided system; however, in high signal-to-noise (SNR) regions with full traffic activity, the ASEs are highest for both systems; by only 0.005 bits/s/Hz/km².