This paper investigates the performance of a pinching-antenna (PA) system with a signal waveguide and multiple pinching antennas to serve users distributed across multiple rooms. The performance of the system is evaluated through a comparative analysis under both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) schemes. Specifically, this paper derives closed-form expressions for the outage probability (OP) and ergodic rate (ER) in each scheme. Furthermore, asymptotic analyses are conducted to characterize the system behavior in the high signal-to-noise ratio (SNR) regime. Extensive Monte Carlo simulations are utilized to validate the accuracy of the analytical derivations. The comparative results can be summarized as follows: 1) in the downlink fixed-rate scenario, whether OMA or NOMA achieves better outage performance depends on system parameters, such as the number of users and power allocation coefficients; 2) in the uplink fixed-rate scenario, the outage performance of NOMA is inferior to that of OMA in the high-SNR regime, and the decay rate of the OP for NOMA users depends on the rate thresholds; and 3) for both uplink and downlink adaptive-rate scenarios, the rate performance comparison of the two schemes depends on system parameters in the low-SNR regime, whereas OMA generally outperforms NOMA in the high-SNR regime.