The performance of orthogonal and non-orthogonal multiple access is studied for the multiplexing of enhanced Mobile BroadBand (eMBB) and Ultra-Reliable Low-Latency Communications (URLLC) users in the uplink of a multi-cell Cloud Radio Access Network (C-RAN) architecture. While eMBB users can operate over long codewords spread in time and frequency, URLLC users' transmissions are random and localized in time due to their low-latency requirements. These requirements also call for decoding of their packets to be carried out at the edge nodes (ENs), whereas eMBB traffic can leverage the interference management capabilities of centralized decoding at the cloud. Using information-theoretic arguments, the performance trade-offs between eMBB and URLLC traffic types are investigated in terms of rate for the former, and rate, access latency, and reliability for the latter. The analysis includes non-orthogonal multiple access (NOMA) with different decoding architectures, such as puncturing and successive interference cancellation (SIC). The study sheds light into effective design choices as a function of inter-cell interference, signal-to-noise ratio levels, and fronthaul capacity constraints.