We compare the achievable rate for QPSK and DQPSK modulations while considering the effect of channel estimation errors and pilot overhead. DQPSK is generally regarded in the literature as the low complexity alternative to QPSK, and is considered to sacrifice the performance as a trade-off. This argument is valid when the channel is perfectly known to the receiver. Here, we show that when the cost of pilot overhead and channel estimation errors are considered, there exist cases where DQPSK modulation delivers higher data rates as compared to QPSK modulation, even if optimal ratio of symbols are assigned as pilots. We classify these cases, and show through simulations that they occur frequently in underwater acoustic channels as the long delay spread requires a considerable pilot overhead for estimating the channel. Our results are supported by analysis, as well as simulation.