The article said thick should be quickly peeled with a vegetable peeler so they cook up quick and bright green. the author claims that without peeling it takes too long to get them tender. Then the thick can be grilled, quick steamed or poached.
The author of the article (Mark Bittman) says that thin asparagus cooks too fast to steam or poach (they get mushy) so he recommends stir fry or roasting these. He also says that since the thin are less fibrous, it's easier to make a quick pureed soup from the thin.
I don't know, I've grilled, steamed, roasted and stir fried both and love them all.