Is the prestige of a university correlated with how rigorous its undergraduate courses are? How much harder is it to get an undergraduate degree (say, in computer science) at a highly competitive university compared to a less rigorous institution?
Your intuition is correct; I nevertheless do not think is it easy to quantify how much harder (or easier) is one degree compared to another. It is imperative to also define how we measure "hardness"; eg. hours per week? success rate? span of material covered? etc.
Clearly one adapts the difficulty of the lecture to the audience. I am not talking about trivializing a topic (that can happen too and it is wrong) but actually as an educator you have to strike the right balance. 

To give a small anecdote from Greece:
My very close friend graduated Physics and decided to go a second degree afterwards in EECS in NTUA. EECS in NTUA in Greece is one of the most prestigious and hardest to get in schools in the country (occasionally it is actually the hardest). In this programme he had to do a particular Physics class and while he was good, he had to put a lot of effort on it. So at some point he asked the lecturer (I am paraphrasing) : "I am a physicist, I know this stuff and I know you give them really hard problems on this subject. I see the class fighting to keep up; is it worth it? It is extremely unlikely they will use this material." the answer was : "Yes, you are right; but they are the best (theoretically) in country so I need to drill them the hardest." The lecturer was adapting the lecture to the audience. And I have heard complains from academics in minor schools for the exact opposite thing (under-qualified audiences).

To recap: Yes, the same class taught in a top school and in a average school will almost surely be harder in a top school. That is natural and should be expected to a certain degree. Quantifying the difficulty of it though is useless unless you have a particular "yardstick*.

Disclaimer: I am not a physicist nor did I attend the institution mentioned above aside a few lectures here and there.