What is the difference between Gaussian discriminant analysis and logistic regression?

Question

As stated in this course pdf, Gaussian Discriminant Analysis (GDA) can also be expressed in the form of $\frac{1}{1+\exp(-\theta^Tx)}$, where $\theta$ is some appropriate function of $φ$, $\Sigma$, $u_0$, and $u_1$. So why can't logistic regression predict model like them?

Answer 1

GDA makes more specific assumptions about the data set then Logistic Regression and if those assumptions are true then it works better then LR. But on the other hand LR makes more generic assumptions and can be more useful in lot of other places where the probability distribution of the feature set is not Gaussian.