Pros: Has the ability to find more local clusters that K-Means would not be able to differentiate
K-Means aims to minimize the Within Cluster Sum of Squares, while EM aims to maximize the likelihood of an underlying probability distribution.
A Gaussian Mixture Model describes an underlying distribution that is composed of multiple individual Gaussian distributions
Expectation-Maximization refers to a two-step, iterative process that is often used when latent or unobserved variables are present underlying a data generation process.
Both QDA and GMM are based on the premise that the underlying data is generated from two or more Gaussian distributions, but QDA is usually used in the supervised learning context, while GMM is used in the unsupervised context.