Congratulations - you have great choices! Take a second and give yourself a pat on the back - you are smart and wanted by top schools.
As I read your initial post, it seems like you placed yourself mentally at UT before the money came in for Rice. I would try to give that fact some self reflection as you think about your decision and take some time. Two great schools. The money is real issue, but if you work hard and succeed as in engineering major, the dollars you mention in your post should not lead to the life long debt many US students face.
Like other posters, it seems to me that Rice is a more unique opportunity. I also can’t help thinking that Rice’s motto, unconventional wisdom is somewhat ironic given your leanings. Good luck. Make sure you enjoy your college admissions win.