Dual-comb spectroscopy (DCS) has shown unparalleled advantages but at the cost of highly mutual coherence between comb lasers. Here, we investigate spectral degradation induced by laser frequency instabilities and improvement benefited from active laser stabilization. Mathematical models of DCS in the cases of direct radio-frequency (RF) locking and optical phase stabilization were separately established first. Numerical simulations are utilized to study the impact of laser intrinsic stability and the improvement by different locking strategies on spectral performance in the following. Finally, both simulations are proven by corresponding experiments. It shows that an optically phase-stabilized system owns a better immunity of laser frequency fluctuations than a direct RF-stabilized one. Furthermore, the performance improvement by the feedback servos is also more effective in the optically phase-stabilized system. In addition, the simulations could instruct optimal design and system improvement.