In this paper we present a unified approach to obtaining rates of convergence for the maximum likelihood estimator (MLE) in Brownian semimartingale models of the form \[ \d X_t = \beta^{n,\theta}_t\,\d t + \sigma^n_t\,\d W_t, \qquad t \le T_n. \] We show that the rate of the MLE is determined by (an appropriate version of) the entropy of the parameter space with respect to the random metric hn, defined by \[ h^2_n(\theta, \psi) = \int_0^{T_n}\left(\frac{\beta^{n,\theta}_s-\beta^{n,\psi}_s}{\sigma^n_s}\right)^2 \,\d s. \] Several known results for the rates in certain popular sub-models of the Brownian semimartingale model are shown to be special cases in our general framework.