Both methods find eigenvalues in the interior of the spectrum, it’s true, but shift-and-invert finds eigenvalues near a given shift μ, whereas FEAST finds them only inside a contour. There is a big difference if there are a lot of eigenvalues you are not interested just outside the contour — ordinary shift-and-invert Arnoldi will pick up a lot of those (and hence require a larger subspace). It’s also a big difference if the contour is very non-circular (e.g. a narrow strip in the complex plane) — basically, FEAST picks an optimized set of shifts for you. As you say, FEAST basically optimizes an “eigenvalue filter” for you.
Caveat: My experience with contour-integral eigensolver methods is mainly for nonlinear eigenproblems, where the competitors’ flaws are much worse. My knowledge of FEAST is only theoretical and from talking with the FEAST authors and looking at the FEAST papers.