m1817 points out the job prospects and networking, which is something you should highly consider into your choice. There are also several other factors that you should keep in mind when selecting the school.
- School atmosphere. Do you enjoy a large public school or a small private school atmosphere? Michigan is much, much larger than Rice and will contain numerous resources and faculty across campus. Rice has a more tightknit feeling and it's often that you'll see many people you know just walking to class. Michigan also has a much larger school spirit in general, unless you're really big into baseball.
- Curriculum. I can't say much about Michigan but Rice has a very flexible curriculum. It both allows and forces you to take classes outside your major. Michigan might have a more variety of classes to choose from because they have more faculty. I would say both schools will be challenging since they're ranked similarly, but the courses and curriculum makes a huge difference.
- Location. Four(ish) years doesn't seem like a lot, but in the moment, you'll definitely be aware of where your school is located at. Houston is the 4th largest city in the U.S., has a huge foundation in the oil/gas and energy industries, and can get extremely hot in the summers (though is very pleasant during the school year). Ann Arbor is a beautiful, mid-size city, and because it's way up North, will probably be the opposite of Houston in terms of weather. In addition, there's a good chance you'll do some work (intern, co-op, post-grad) where the school is located. If you have a big geographic presence, this could be extremely important.
- Campus life. As mentioned, Michigan is big on sports. With such a high population, you will also probably find a large variety of students and many different activities to do. You might also feel a bit lost in the crowd sometimes. At Rice, campus life mainly revolves around the residential colleges, which most people enjoy because you get to know everyone you live with. At the same time, some people think this makes it hard to meet people outside your dorm and if you don't like the people you live with, you could feel like you're stuck for a few years.
- People. You'll definitely find spectacular characters at both universities. Michigan you might find a wider variety of students in the spectrum because of the sheer size. At Rice, I personally find generally, students are extremely diverse, well-rounded, and multi-dimensional. Though I wouldn't be surprised if there were certain people or attributes of people that you would find at Michigan who aren't represented at Rice. Also, does it matter to you the size of the percentage of international students? I think both universities are just over 10% of the student body, but Rice seems to contain a lot more from the Asian countries. The demographics is also quite different in the two schools, which may also influence your decision.
Honestly, I would say ignore the rankings and go with the intangibles. You’ll be challenged at both schools and both schools will open up doors for you. But nothing will replace the experience of four years at college.