The joint transmit and pinching beamforming design for spectral efficiency (SE) and energy efficiency (EE) tradeoff in pinching-antenna systems (PASS) is proposed, under practical channel and energy consumption models. In the single-user scenario, it is proved that the optimal pinching antenna (PA) positions are independent of the transmit beamforming. Based on this insight, a two-stage joint beamforming design is proposed. Specifically, in the first stage, a general PA placement framework is proposed for multi-waveguide systems. In the second stage, the closed-form solution for the optimal transmit beamformer is derived given the optimized PA positions. In the multi-user scenario, an alternating optimization (AO)-based joint beamforming design is proposed to balance the SE-EE performance while taking the quality-of-service (QoS) requirements into account. It is proved that the proposed AO-based algorithm is guaranteed to converge when no constraints are violated in PA placement subproblem. Numerical results demonstrate that: 1) the proposed algorithms effectively improve joint SE-EE performance; 2) PASS exhibits strong robustness against variations in the service area along the waveguide direction.