Both. It depends on the need. Both are fever reducers and MILD pain relievers. Ibuprofen (motrin) is also an anti-inflammatory...so works on inflammation and muscle pain in a way that tylenol doesn't. It also lasts for 6 hours as opposed to 4 for tylenol. But tylenol works faster on pain and fever. You know if tylenol isn't keeping a fever down, it's a massive fever you're dealing with (104-106 unmedicated).
You can take both of them together...but we don't unless a fever isn't controllable (stays in the 100-102 range) with one alone.
Caffeine also makes Tylenol more effective (remember "Excedrine the Headache Medicine"? Just tylenol and caffeine). Caffeine has no real effect on ibuprofen.
If there's severe swelling (say in a sprain or with teething), you'll get a lot of swelling relief from ibuprofen, but not a lot a pain relief. When I have a sports injury, I take both...the ibuprofen for the swelling, and the tylenol for the pain. But if there's NO swelling, you'll pick up the pain relief. And if it's something like cramping, ibuprofen is better, since it goes after the muscles first...but for the pain of teething/sprains/etc it's tylenol. I'm always walking a balance between swelling v pain (like fever a LITTLE swelling is a good thing). So like I said, we vary by need.
Obviously, if one doens't "work" don't use it. My mum and my sister are actually allergic to acetaminophen (tylenol) and can't take it at all.
REMEMBER REMEMBER REMEMBER...Go by WEIGHT not by age. We're scandanavian (aka big...I'm 6'1" and I'm the shrimp in the family), so our 2 year old could weigh twice as much as a Japanese two year old. My cousin was giving her daughter tylenol by age, and actually needed to almost triple the dose when she looked at the chart that had WEIGHT on it. Oops. Also, the limit is lowballed on the box. When we have a massive fever and are already combining the two I always call into Children's Hosp to get the ACTUAL max doseage for my son's weight.