I think all butter can make a cookie crispier and a bit of shortening keeps them softer.
I used to use all butter, but now when I make a softer cookie, like oatmeal, I use 1/2 shortening and I think it does keep mine softer. For crispy cookies, I use all butter. For Snickerdoodles, I think it doesn't matter cuz the cream of tartar gives them that nice softness with crispy outside that everyone loves.