So, aspirin is derived from willow bark, a natural substance whose analgesic properties have been known for a long time, with some of the earliest recorded recommendations for its use coming from Hippocrates (or that chick in Clan of the Cave Bear, but she's fictional and doesn't count.)
But aspirin is also an anticoagulant and some folks are allergic to it and too much can cause ulcers and may contribute to kids' brains swelling up and stuff, and so acetaminophen was invented. Instead of those side effects, it just destroys your liver if you take too much over too short of a time or, apparently according to a recent study, destroys your ability to give a damn about the problems of others.
Liver-damaged zombie or hemophiliac ulcer patient in convulsions*... That'll put you right off reading the warning labels more, won't it?
*I am way exaggerating this for the yuks. Chill. Although I prefer aspirin to Tylenol myself.