Three dimensional shape matching plays an important role in many of today's applications. Nevertheless, shape matching is a difficult problem since there is no unique measure that defines shape similarity and since computing shape distance using various measures is an elaborate task. In this paper we present a new framework for matching shapes, represented by union of spheres hierarchies. Our approach is "feature-sensitive" since it extends the usual geometry-based matching by adding sensitivity to shape topology, shape features (sharp angles, chemical attributes) and their relative positioning on the shape. Our method can be used in conjecture with other geometric matching methods as a pre or post-processing filtering stage, or it can be used as a stand-alone feature-sensitive matching.