Let me guess OP, you are a Brown legacy. That is why you got in there and not to other comparable and schools that fit better with your goals. That Brown legacy thing works well for wealthy offspring. Tell me I am wrong!
You are correct about Brown and engineering, including computer engineering. Even if US news does not give it a poor ranking, rankings that don’t consider school’s reputation don’t rank it well. QS World University Rankings by Subject 2014 - Computer Science & Information Systems does not list it in the top 50-and that is CS not computer engineering.
But that’s not your question. Yes you are better off from Brown then from a a lower ranked school as a general rule but not necessarily in your case. If you nailed your engineering classes at RPI and nailed your history class at Brown-you’d have a better shot from RPI. The post listed above is also incorrect about CS at Penn. Yes it is stronger than Brown.
Wanting a school that is a better fit for your interests is certainly a reasonable rationale for transferring. The question is how realistic it is that you’ll get into any of the schools you want. If I am correct about your legacy status, chances for the very competitive ones are small. If I am incorrect, then you may have a slim chance. Not to MIT or Stanford unless you get national recognition for your accomplishments in the next year (when you wrote “AIME qualifier, ranked 4th in county” you meant county right, not country?). Short of that, your best bet among the schools like those you’ve listed are Cornell, Penn, UC-B,. Might also try Georgia Tech, VT. Naturally there are others. I 'd go to Brown unless you know you can Ace the most rigorous courses at RPI to enhance transfer potential. But, if you are willing to give up on the most competitive schools, graduating with an engineering degree from RPI is nothing to sneer at.