Considering imperfect successive interference can-cellation (SIC) for non-orthogonal multiple access (NOMA) communications, this work studies the cooperative reconfig-urable intelligent surface (RIS)- and relay-assisted system under Nakagami-m fading. We focus on the performance comparison for such cooperative schemes, under different channel conditions and system parameters. To achieve an equivalent capacity for these two schemes, the minimum required RIS elements number is determinated under high signal-to-noise ratio (SNR). Simulation results demonstrating the reliability of the analysis, validate that the relay-assisted scheme is superior to that of RIS-assisted one when the RIS elements number is small and transmitted power is lower. The results also confirm that the deployment of RIS should consider the actual situation of the application scenario.