It IS interesting that Lindsay's trashed but Keira isn't as much...
I think it's because Keira hasn't been involved in much drama. She's British, she lives in London, not L.A., so she isn't seen as much at hotspots there, whereas Lindsay lives in a hotel in west L.A. and hits the club circuit quite often. Keira doesn't hang with Paris Hilton, hasn't gotten into a feud with another celebrity (Lohan & Duff), doesn't talk about her sex life in interviews, and hasn't dated high profile men who have talked about her (her last BF is a model/actor, sure, but he isn't A-list yet, nor is her current beau). Lindsay's first serious public boyfriend blathered about having sex with her to the public, adding fuel to the fire. Also, Keira is known more as a "serious" actress, despite box office bombs like "Domino" and "The Jacket." Lindsay is known more as a "teen queen," though she hates that term. "Mean Girls" made her career take off, but it also pigeon-holed her into that type of role.
In interviews Lindsay talks about sex, has had very public family trouble, and has even made a music video about it. Lindsay seems to invite the attention. "I admit, I love [the attention]," she said in an interiew. Keira tends to be more quiet about it in comparison.