Both Stories are amazing, and it is quite difficult to choose who is better than the other.
Though Fone does not seem like a normal design for a hero, he makes up for it with an amazing courage to fight the enemies who threaten to enslave the world and shows to have a heart of gold even if his cousin, Phoney, is a major schmuck who started all of the trouble. Out of many heroes who do not have any special powers or magic weapons besides their wits, valor, and friendship with dragons, he turns out to be one of my favorites. In the end he won the girl, a very scary, lovable warrior of a girl.
The other hand, Frodo is a cool character design with a interesting story line that kept me hooked to the series. I liked how he was brave at times, but on other cases he became the damsel in distress, hid from his enemies with the help of the ring or gave into corruption of the ring he was to dispose of. Although he is lovable, his group made more of an effort than he did.
Yeah, that's a hard choice, but I have to go with Fone Bone, if only because the Bone comics were a huge inspiration for my art (not that LotR wasn't, but in a different way). In a one on one fight though I'd have to go with Frodo. He's got the One Ring, Sting, and his mithril shirt of badassery +6, while Bone's got...flexible muscles. Hmm.