Two very different schools.
Rice is urban in a major city, very diverse and International. Small, private probably opportunities to research, intern, etc. strong path from an elite school into Ph.D. Programs. Beautiful campus in the museum district which is a great area. Easy to get around Houston.
Michigan is a huge public school with multiple campuses that are quite large and impressive. Nice college town not far from Detroit (not a thriving city). You will be with many thousands of instate Michigan students. Many very solid academic programs. Perhaps large classes and competition for resources and placement.