Most of the metric differences between these schools are minimal since both have premiere engineering programs associated with massive R&D budgets (Rice’s budget is much, much smaller though as discussed below) and huge medical programs (hence they both have stellar BME programs). Both schools are known for their engineering programs overall if you do decide to switch majors. In terms of ranking surveys given to key opinion leaders, which have limited value in terms of metrics an undergrad should care about (faculty size, research opportunities, career support, academic advising), JHU is ranked #15 for Best Undergraduate Engineering Programs and Rice is #18 - a negligible difference (http://premium.usnews.com/best-colleges/rankings/engineering-doctorate/page+2). Again, both programs are stellar for any engineering, and what truly will affect career success, PhD placement, etc. is not which program you enroll in but rather your success at either school. If you do well at either school (strong research experiences, rec letters, good grades) then there is no reason why you won’t succeed in your future endeavors. Ranking differences of a few (even 10-20, honestly) have little to do with outcomes and simply mean they will provide you similar resources and opportunities for you to take advantage of. The rest is on you.
You do want to be happy at whatever school you attend, but again, that has less to do with the school and more with you. I was a premed Neuroscience major at Hopkins, as competitive as it will get at our school, and there was NO cutthroat behavior (no lab sabotages, no hiding library reference books, etc.). None of the shenanigans that are constantly rumored were ever seen by me or anyone I asked past or present who actually went to school there. Every assumes and the rumor perpetuates itself. Yes, the school is competitive. Students work very hard and most people naturally put pressure on themselves to study longer as they see their peers working diligently. I saw this as a great motivator and worked even harder, but it was a collaborative setting and was never mean-spirited. You can look at new building designs on the JHU campus including the Brody Learning Commons or Malone Hall and see that they are large open floorpans designed for collaboration and interdisciplinary research. This produces the best research and the best learning outcomes and is how the world operates. People don’t work alone and so JHU (and most universities I’m sure) emphasizes group projects, group learning, and team-based problem solving. Basically, don’t discount JHU based on rumors of cutthroat behavior since it simply isn’t true.
Also remember that actually going to a school that is stress free (and I can tell you students in the Rice BME program are not stress free, that’s just naive to think) may not be such a good thing since life is stressful, work is stressful and grad school is stressful. Learning early on to manage stress in a healthy way and learning skills like time management, organization, etc. will lead to better outcomes and a healthier life. Don’t worry about stress and competition because these will occur in any stellar program at any great school, it all will depend on you and how you handle the stress. If you’re around people who are stressing you out and not contributing to your learning process then find new people to study with. It’s that simple. Don’t let these false stereotypes be the basis for why you pass up on JHU.
If you want to get picky, the Hopkins Healthcare system is larger and more prestigious than either the UT Houston or Baylor Medical programs associated with Rice. I’m not sure how well Rice is integrated with the UT & Baylor system since Rice technically does not have its own medical school, but I suspect it is well integrated given the stellar BME program. Additionally, both are considered large research universities, but Hopkins does have a significantly (significantly!) larger overall R&D budget and engineering budget than Rice http://www.bestcolleges.com/features/colleges-with-highest-research-and-development-expenditures/. I will disclaim though that a significant portion of the overall R&D at Hopkins and its engineering budget are dedicated to the Applied Physics Lab (about 1.1 billion dollars, half) which is 40 minutes away from the undergraduate campus. Undergrad students do conduct research at APL (engineering, primarily), but there are significant barriers to those resources. Most likely BME research would not be conducted there, and even if it were, you probably wouldn’t be willing to drive there, so I wold cut the JHU R&D budget in half when comparing. Even then, JHU clearly has a larger budget compared to Rice, which does not rank in the top 50 in terms of R&D budgets, which can be translated to more opportunities for early and more meaningful undergrad research (again though, both schools have stellar research programs).
As for specifics, I’ve heard from other JHU BME posters on this site (and witnessed from my friends who were BMEs) that the program emphasizes design. Most students will take a prototype design class their junior or senior year that has you work with medical staff from the Hopkins Med School to solve a real-world problem by designing a prototype. Students have gone on to market these products, so this truly is a real-world, meaningful experience. Hands-on learning that addresses real world problems with meaningful outcomes (an actual prototype) is what a strong engineering program should do to prepare you for a career in engineering, and the Hopkins BME program does this well. I’ve also heard students praise the program for its actual teaching of BME content. Many engineering schools teach BME as a mash-up of basic engineering courses and then biology courses and try to jam it together, but Hopkins truly does teach courses from a BME perspective and integrates the content well as a unified topic rather than some chimera of biology and engineering. I cannot speak to Rice about this, but I’m sure being ranked #4 in BME they offer similar benefits.
Regarding more general things, both schools are located in major cities (Houston is the fourth largest city in the U.S. with over 2 million people and Baltimore has about 620,000 people, fourth largest on East Coast). There is plenty to do in both cities with your free time. I can’t speak to Houston specifically, but I can tell you I had a blast in Baltimore. Additionally, the East Coast has tons of other neighboring cities like DC, Philly, and NYC which are all weekend getaways (DC is only 45 mins away) that I managed to fit into my hectic schedule multiple times. Houston, on the other hand, is a little more isolated with Dallas, Austin and New Orleans being the major cities worth visiting nearby that are 3-6 hours away. The East Coast does offers better transportation options than the South.
As for income data and ROI, I know JHU constantly ranks lower than many other schools and I’m curious to know what the impact of having the highest per capita of premeds would have on 20 or 30-year net incomes given close to a quarter of JHU students are going the premed route, which (when including two gap years, less than the national average of four gap years) has students going to school/training/applying for another 8-12 years after graduation with limited income during residency and $100,000s in debt. Unless you can find specific data on engineering majors (or at least some way to account for the significantly higher than average premed numbers), income/ROI data seems to be of limited value.
Some other general info on Hopkins can be found on these threads:
Safety: http://talk.collegeconfidential.com/johns-hopkins-university/1821701-questions-about-baltimore.html#latest
Social Life, Things to do in Baltimore, etc.: http://talk.collegeconfidential.com/johns-hopkins-university/1878658-johns-hopkins-vs-cornell.html#latest