I know that $\frac{1}{n-1}\sum\_{i=1}^{n}(X-\bar{X\_{n}})^{2}$ is an unbiased estimator for the variance.

I thought of such an estimator to be useful when it is not know from which distribution the data at hand are coming from.

Now given I have a data set and I do know which is the underlying distributions of the observations. Shouldn't I prefer a Maximum Likelihood Estimator for the variance even if it is biased since it obviously makes use of the underlying distribution of the data over the general variance estimator cited above, which is not for any specific distribution?

Thanks