Differences between Fuzzy C-Means and EM
The difference between the two schemes is the model of the clusters. Fuzzy C-means and K-means model their clusters as circles (spheres in n-dimensional space), EM-clustering models the clusters as probability density functions (PDFs). In Euclidean space, the latter can have elliptical shapes (using Gaussian PDFs), determined by their covariance matrices.

Thus the difference is that the assignment criterion for K-means is the distance to a centroid whereas the criterion for the EM-algorithm is the probability of a data point given the PDF of the cluster center.

The cluster centers in K-means are hard-assigned, in Fuzzy C-means they are not; but it is rather simple to get a hard decision by, as you stated, taking the cluster with the highest probability/smallest distance for a given data point.