Due to complexity considerations, pulse-hased modulations such as pulse position modulation (PPM) and on-off keying (OOK) are well suited for wireless sensor networks (WSNs) since they provide the possibility of carrier-less signaling and, more importantly, non-coherent reception bypassing channel estimation at the receiver. In this paper, we compare PPM and OOK in terms of their battery power efficiencies (BPE). using a nonlinear battery model, and under the same bandwidth efficiency and cutoff rate constraints. Cutoff rate is employed as our comparison criterion because it leads to a tractable analysis that is often impossible through direct evaluation of random coding exponent or capacity. In addition, cutoff rate gives a universal expression for both coherent and non-coherent detection by simply setting different channel state information (CSI) qualities. Our system model integrates typical WSN transmission and reception modules with realistic nonlinear battery models. Circuit power consumption. DC/DC converter efficiency and power amplifier efficiency are also taken into consideration. Our analytical results characterize the signal-to-noise ratio (SNR) - cutoff rate - CSI region where PPM (OOK) is more power efficient than OOK (PPM). We provide an interpretation in terms of transmission range and symbol set size. Numerical results verify the analysis.