We use theoretical models to compare the receiver signal to noise ratio (SNR) vs. average rate of detected signal photons for an integrated path differential absorption (IPDA) lidar using coherent detection with continuous wave (CW) lasers and direct detection with sine-wave and pulse modulations. The results show the coherent IPDA lidar has high receiver gain and narrow bandwidth to overcome the effects of detector circuit noise and background light, but the actual receiver performance can be limited by the coherent mixing efficiency, speckle and other factors. For direct detection, using sine-wave modulation allows the use of a low peak power laser transmitter and synchronous detection. The pulse modulation technique requires higher laser peak powers but is more efficient than sine-wave modulation in terms of average detected signal photon rate required to achieve a given receiver SNR. We also conducted experiments for the direct detection cases and the results agreed well with theory.