Hmmm hard. But Bilbo was very reliant on his ring, I don't know how he would stack up in a battle without it. Frodo wasen't fighting alot either but he was always the more adventures one of them (before either of them had traveled outside the Shire) so that might give him an edge. I would say Frodo, barley.
Ok, im going to vote Frodo aswell maing it 4-1!
Now these next rounds are going to be a horse based with quite afew rounds.
Match 1
ROUND 9
Arod, Gimli and Legolas' Horse
VS
Felaróf, The great horse of Eorl
ROUND 10
Hasufel, The horse of Rohan that bore Aragorn
VS
Asfaloth, The horse of Glorfindel (and Arwen)
ROUND 11
Bill the Pony
VS
Snowmane, The swift horse of Théoden
ROUND 12
Shadowfax, The grey-silver steed of Gandalf
VS
The Ringwraiths' Horses