Are the classes that top-tier school such as Harvard and MIT "harder" than classes are lower tiers?

If you can visit, sit in on classes. That will give you the most information about any particular school you are interested in. Generally there is a difference between schools, but that difference doesn’t always match various rankings and may not be totally correlated across all majors. (College A may not be more in depth than College B for every major.)

Also, the difference may mainly be in the freshmen classes based upon the expected knowledge of incoming freshmen with the higher level of depth from some courses being covered in later courses instead.

I know there was a local cc Bio Prof who told his students that his course was the same exact course they would get anywhere they went to college. One of my lads was in his course. That same lad sat in on his brother’s course at a higher level (Top 30ish) Research U and was astounded at the difference. He called his own course (the CC course) Bio-Lite ever after. The difference? He told me his class talked about a topic saying, “There’s an enzyme that helps with this process…” and his brother’s class on the same topic discussed multiple enzymes (8 or 9 I think), by name and exactly what each did. Since I know the prof I opted to take him a copy of the first test from the higher level school. It took him about 30 seconds to figure out what he had been telling his students wasn’t true. He now tells them his course will replace many college Bio 101 courses, but not all. It depends upon where they go.

I know similar things are also true in math courses (tougher Calc problems, etc). CS and other classes? I have no first hand info. Sit in on classes if you can.