@monydad : I agree with some except for the “stats of incoming students”. I never hear of faculty saying: “oh wow, SATs and class ranks of the only 25% that reported have sure gone up from their already high levels, maybe I should change the syllabus or put significantly harder problems on my exams”. You can actually access course websites from an instructor and notice that many are nearly at the same level before and after a period of time in which their was/is a huge change in admissions selectivity (what may happen is the averages for the exams go up over time). Unless there is some big (usually external) change, things don’t change drastically or at all. I could actually demonstrate this using the course websites of a faculty member for w/e staple course at both of these schools and some others, but I won’t waste my time.
I think simply looking at the course work if available is the best indicator when comparing two high caliber academic institutions and also tells a student what they may be getting into (ideally, you can get multiple sections/faculty if a course isn’t standardized across sections). I suspect that class sizes, some minimum threshold of selectivity/stats that indicates “generally high achievers go here”, and investment (some schools have a track record of seeking large grants for this purpose) in reforming STEM education predict how challenging the courses will be and what style of challenge a student will receive. Unfortunately, once the school is already highly selective, whatever the admissions office is doing to help even further increase those stats (mainly to hopefully increase the rank) will not really transfer to what happens in STEM classrooms, or really any classrooms.
Most elite schools will have a good baseline of rigor in STEM though, but stats can hardly predict the better among them especially after admissions offices deliberately change their strategies and focus for who knows what reasons (let us not pretend that all the new Harvard level SAT/ACT schools just suddenly became that way organically). For example, Stanford STEM must have become less rigorous than Vanderbilt, Rice, Hopkins, and many other top private schools who, in the past 5 years have decided to focus more on the SAT/ACT ranges in admissions and have thus surpassed Stanford in at least the bottom quartile and maybe even both the bottom and top quartile (note that class ranks at Stanford are very high, but what does that mean when 20-30% report each year?). And now, you have a larger number of schools below 10 in USNWR with nearly identical (or higher) SAT/ACT ranges versus Harvard, Princeton, Yale, and MIT, so we must thus assume that because of this change, that their STEM curricula evolved to, on average, catch up to or surpass those places. I’ve seen some of the courses, and this just isn’t the case. It also basically says, “Chicago must be way more rigorous today than 20 years ago when it was less selective than its close ranked peers”. It just doesn’t work.
In general, one should just assume that they will be challenged and stressed as an engineering major at any school designated (and has been for a decade at least) as “very selective” or “most selective” no matter if students from one school shout their difficulties on top of a mountain more than others.