<p>The name of your undergraduate school matters far less than what you do while you’re an undergraduate. The important point, then, is to pick the school that will allow you to accomplish everything you think you might ever want to do as an undergraduate.</p>
<p>You won’t be able to do everything you might like to do. You probably even shouldn’t for your own health. What you’ll end up doing will be a random sampling of all the things you might have done, and hence going to a school with fewer opportunities for you could mean–if that random sampling isn’t very good–that you don’t get much done.</p>
<p>In your case, both Stanford and Rice have an incredible number of opportunities for undergraduates. I agree that Stanford is more prestigious than Rice, but I truly think it’s a very subtle issue as to whether there are more opportunities at Stanford for undergraduates–this is one of Rice’s main strengths. I think it will depend heavily on your specific field and how advanced you are in this field. (Unfortunately, I don’t know enough about electrical engineering to give you good recommendations on this.)</p>
<p>In short, the difference in prestige between Stanford and Rice is going to be nearly if not totally irrelevant in your graduate school applications. So pick the school that will help you make the rest of your applications–the parts that don’t consist of your school’s name–good.</p>