In my experience, it is more nuanced than even that. Just take computer science. There are schools that teach languages. You'll spend a semester with C, then a semester with C++, then one with Java. And then there are colleges that teach concepts. Let's look at memory management (and pointers), then let's look at data structures, then let's look at networks. Personally, the latter seem to be a far better education even if the overall experience leads to less initial skill at any given language.
Or take a look even with the same college between degrees. Some science tracks requires statistics for business majors where they will spend a day learning how to sum numbers. Other science tracks require statistics for science and engineering, where multi-variable calculus is a prerequisite. Now imagine if the degree requiring the simplified statistics was switched to requiring the harder version.
(All this being said, I agree connections are a bigger deal. I think what you learn does differ between colleges, but at the end of the day it isn't what you know but who you know.)