Yes, the styles are very different. There wasn't anything in the sound, really, that made me make the comparison, but I realized that I was listening with something like "Ashlee activeness," wanting to understand this person's particular iteration of life's mess. This is very different from Avril, who's too obtuse for much deep listening from me, and even from Kelly, whose anguish codes an easier form of Tragedy. Demi and Ashlee both specialize in the "hair is a mess and my life is completely fucked" style of tragedy, so in that way I think something like their mode of address(?) or maybe M.O. is similar even if their sound isn't all that similar.