If you fly mostly business or first class, LH Miles and More is the way to go. If you fly economy class a lot, I think UA's Mileage Plus would be better as they give miles for most economy booking classes. Besides that, its really a personal preference and where you live. If you live in a country with a dominant star alliance carrier, you might want to join their program, as they might have other earning oppurtunities, like through credit cards, etc.