Well let's see here. Linkin Park had a few good albums, Meteora being the best. Their new stuff sucks ass. Fall Out Boy only had one good album, From Under the Cork Tree. Everything pre and post-Cork Tree was awful.
I'll have to go with Fall Out Boy only because I still have them on my Zune and still listen to From Under the Cork Tree. I only hear stuff from Linkin Park when I go to my friends house and don't have enough motivation to listen to them regularly. I wonder if my opinion really matters though since I think both are terrible these days.