If you take them often enough you should research this, but off the top of my head acetaminophen (Tylenol) damages your liver while aspirin is recommended to the elderly as a long-term "maintenance" drug to reduce cardiovascular problems. On the other hand, it's an overdose of acetaminophen that kills your liver, while aspirin can cause things like internal bleeding.

As usual, you pick from a menu of risks and you choose what's best for your particular situation.