Indicates that the speaker identifies with a prior statement to a much lesser degree (or not at all) than the other person.
My mom really likes spinach; me, not so much.
Indicates that one factor is much more relevant or important than another.
It's not so much that he's a bad person, but that his political views are too extreme.
It is not so much our friends' help that helps us, as the confidence of their help. Epicurus
Success is to be measured not so much by the position that one has reached in life as by the obstacles which he has overcome. Booker T. Washington
The difficulty lies not so much in developing new ideas as in escaping from old ones. John Maynard Keynes
Beauty is not so much what you see as what you dream. Walloon Proverb
Not so much that it burns the saint, nor so little that it doesn't illuminate him. Mexican Proverb
We are not so much concerned if you are slow as when you come to a halt. Chinese Proverb