We investigated experimentally and theoretically the mode competition and output power characteristics in terahertz second-order distributed feedback quantum cascade lasers. The experiment results demonstrated that the lasers operate stably on the fundamental transverse/longitudinal mode during the whole laser dynamic range. High-order transverse modes are suppressed due to the absorbing boundaries set along the laser ridge. In addition, the fundamental mode and the high-order longitudinal modes are very close in frequency, and their electromagnetic fields have strong overlap. The spectral or spatial hole burning effect is therefore effectively avoided, leading to a stable operation of the fundamental longitudinal mode. The experimental results also show that the slope efficiency of output power decreases with the length of the distributed feedback grating. As a result, only in certain grating length, the output power reaches its maximum. Our work provides experimental and theoretical supports for the studies of high performance THz lasers and the phase locked laser arrays.