Instead of carrying acetaminophen and aspirin seperately I carry Excedrin Migraine - acetaminophen, aspirin and caffeine all in one convenient tablet.
That combo of ingredients in Excedrin is apparently great for headaches and migraines (and probably other sites of pain). Unfortunately, I get a painful stomach ache whenever I take any aspirin, so I learned long ago that Excedrin is not for me. Pity. So I carry both acetominophen and ibuprophen tablets in one of those little lip balm-sized travel cases with me most of the time.
And in situations where aspirin use would be discouraged, like with a sick child with a fever, a combination medication like Excedrin lacks the flexibility of separate medications. But, as with most things in life, there's always a trade off somewhere in any choice.