Underwater acoustic communications (UAC) channels are widely perceived as being doubly selective in both time and frequency domain. Basis expansion model (BEM) is an approximation of the time-varying channel with a parsimonious set of BEM coefficients, which facilitates coherent and differential schemes resilient to doubly selectivity of UAC channels. Different BEMs not only approximate the channels with different accuracy levels, but also induce different effects on the model fitting bias and the additive noise. In this paper, we will first show how our previously proposed coherent and differential schemes based on discrete Fourier transform (DFT) BEM can be modified to accommodate other BEMs. We will then analyze the tradeoff between the channel modeling accuracy and bias/noise effect. Our analyses, simulations and experiment results confirm that BEM is a powerful tool in UAC. Additionally, in the choice among various BEM options, not only the modeling accuracy has to be considered, the nature of the model fitting bias and the noise effect also have to be taken into account.