The spectral and energy efficiency (SE-EE) trade-off in pinching-antenna systems (PASS) is investigated in this paper. In particular, two practical operating protocols, namely waveguide multiplexing (WM) and waveguide switching (WS), are considered. A multi-objective optimization problem (MOOP) is formulated to jointly optimize the baseband and pinching beamforming for maximizing the achievable SE and EE, which is then converted into a single-objective problem via the ε-constraint method. For WM, the problem is decomposed within the alternating-optimization framework, where the baseband beamforming is optimized using the successive convex approximation, and the pinching beamforming is updated through the particle swarm optimization. For WS, due to the time-division transmission and interference-free nature, the pinching beamforming in each time slot is first adjusted to maximize the served user channel gain, followed by the baseband power allocation. Simulation results demonstrate that 1) PASS outperforms conventional antennas by mitigating large-scale path losses; 2) WS leads to a higher maximum achievable EE by activating a single RF chain, whereas WM yields a higher SE upper bound by serving all users concurrently; and 3) increasing the number of users substantially enhances SE under WM, whereas WS shows more pronounced benefits in low-signal-to-noise ratio regimes.