Key is to look at the active ingredients;  Tylenol's is Acetaminophen, where as, Advil's is Ibuprofen.  The two chemicals react differently in the body.  Not going too deep in the geek-o-meter, short answer would be to try both (at different instances of course) and see which one your body responds to.  

For kids, Acetaminophen is given mostly for low grade fever (<102) and Ibuprofen for higher grade (>102).  But again this might not be case in every situation.

Furthermore, keep in mind that Ibuprofen works well against inflammation but can also be hard on your stomach, i.e. not an ideal choice if you have ulcers.

Finally, whichever one you choose, buy generic.  Save money without losing quality.