They both wrote so many classic songs its ridiculous, but I've always like Lennon's songs better. His seemed to have more of an edge to them, while some of McCartney's can sound like kids songs, but I wouldn't argue with anyone that picks Paul, its simply a matter of personal preference. I also prefer Lennon's solo work to Paul's.
Also, don't sleep on George Harrison that dude wrote some classic shyt as well like 'Taxman' , 'While My Guitar Gently Weeps' and 'Something' and also put out some great solo work as well.