Rice, unlike MIT, is not an acronym, so not all-caps.
Agree that you are getting way ahead of yourself, worrying about the decision you’ll have to make if you get into both MIT and Rice, when both are massively difficult to get into. Also, your chances of getting into Rice will be significantly greater if you apply ED, but if you get in that way, the decision will already be made.
If you’re a student with the critical thinking abilities necessary for both of these schools, then take a step back and look at the flowchart of decisions you’ll need to make over the next three years. I think you’ll see that you’re skipping way ahead to a decision that you’ll most likely never face. As Momrath pointed out, the question of whether you want a professional BArch program or not will be important in deciding where to apply. (And Rice is indeed one of the very top programs in that category; in addition to the overall quality of the school and program, the preceptorship year is a huge draw.)
Also, your perception of the financial situation, focused as it is on real estate decisions, might really be swerving around the core issue of affordability. Would you get any need-based aid at either of these schools? Run the Net Price Calculators for MIT and Rice (not because they’re your most likely destinations necessarily, but because they will give you a best-case-scenario view of your financial aid prospects - if these fabulously-well-endowed schools aren’t going to give you need-based aid, no place else will either.) Look at the out-of-pocket and have a realistic discussion with your parents about whether you should be pinning your hopes on elite private universities with little (Rice) to no (MIT) merit aid available.
It’s great that you are planning to do a summer intensive. Beyond that, I’d suggest putting your energy into learning more about schools that aren’t super-reaches, that you could still be happy to attend. There are some excellent programs that may be more attainable, both admissions-wise and financially. If a “dream school” works out, great, but identifying those is the easy part. Find matches and safeties to love, and your journey to college over the next few years will be vastly happier and less stressful.