Does course difficulty correlate with college ranking/prestige?

[naturally_curious]

So far I've heard the following assertions :

1. Top private (Duke) is slightly harder and goes into more depth than good state school (Purdue) in biology

2. Top private is ridiculously harder than community college (many community college students don't care)

3. Harvard is harder than MIT

So my question is : how does the difficulty of the course of study vary depending on college rank? Is Harvard always and everywhere harder in most if not all courses relative to the same courses at other institutions? I've noticed that for math, a community college would have linear algebra and calculus as the final courses in the department, whereas both would be first year courses in an ivy league college.

How much variation is there between say, Duke and Harvard -- I'm guessing the difference is smaller compared to 1 or 2, but I've seen people argue that Harvard is harder than MIT, so I'm confused.

[AP]

Since Any information on both rankings and difficulty can be hardly reliable, a) there is no correlation and b) if there were, that’s not useful information.