I dreamed up the two sentences. I don't know that in 'X not to mention Y', whether X is a bigger benefit or Y is. Let's assume that increasing job prospects is a bigger benefit than building social networks. In this case, should I use Sentence 1 or Sentence 2?
- Higher education offers an environment to build important social networks, not to mention increases job prospects.
- Higher education increases job prospects, not to mention offers an environment to build important social networks.
This idiomatic construction does not necessarily mean that the mentioned matter is bigger than the unmentioned one - merely that it is sufficiently important that there should be no need to make a second point.
It can be used to refer to reasons against something as well as for it, so it isn't always about weighing benefits - it can be 'pros' or 'cons'.
The second item should be at least as significant as the first. In your case, if job prospects are more important, sentence 1 is more appropriate.
"Not to mention" doesn't necessarily imply a difference as extreme as similar phrases like "let alone," but it still loses some of its rhetorical impact when reversed.
This can go either way. Usually, X is more immediately applicable to the subject at hand, and more specificially to the point.
"Using this gasoline will make your car run better, not to mention lower cost."
However, the construction can also be used ironically, when the less immediate aspect is also generally more important.
"Switching to solar power will lower your electricity rates, not to mention helping to save the planet."
So, there really isn't a yes or no answer to your question.
