The two primary assumptions of DFA are multivariate normality and equality of covariances. There are some suggestions that logistic regression is less sensitive to differences from normality, and that if you have only 2 groups, that is the preferred technique. So it's really up to you. If you have more than 2 groups, DFA is the only choice. When to use it, and when to use logistic regression I just want to talk very briefly about logistic regression.
Logit analysis is regression of a series of independent variables on a binary dependent variable.
This is still fairly rare, because few people have the tools and skills to work with it. There are forms that use logit regression and forms that use discriminant functions, but basically what it does is to help understand structure in complex data sets. Logit regression is a hierarchical dichotomous technique based on intensive succession computations. For discriminant analysis, it would be the variable that best separates the group means. It then takes those subsets and redivides them, and so on.