Bilbo was brave, with Smaug and BO5A, but Sam battled Shelob, toiled through Mordor knowing that he would probably not survive to see the things he was trying to save, and even carried Frodo to Mount Doom.
I voted for Bilbo simply because I feel like it took more courage for Bilbo to leave the Shire than Sam. Sam is brave when faced with a situation that demands it, but Bilbo left his home with a group of strangers to face a dragon.
Sam had heard of Bilbo's adventures, plus he had Frodo to go with, and several other hobbits before they even got out of the Shire proper.
I just think it was more of jump for Bilbo to go have adventures than it was for Sam.
I would say Sam, though he hasn't the impertuosity of a Took which clearly Bilbo inheritated, Sam Gamgee could have avoided the whole thing and stay peacefully gardening in The Shire or at least turn back from Rivendell and gone home. But he stick all the way with his Master Frodo and his companions and faced the hopeless journey to the bitter end. That's what I call been brave. He did have a way out of this many a time but decided to go on and face the challenges. He didn't need to be roused like Bilbo, who given the opportunity would have stayed quietly at bag end and got lucky finding a magic ring. That doesn't mean he is not brave but I think Sam facing Shelob and raiding the Orc Tower wins it here. He was driven by his love of his master.
(This post was edited by sam90 on Jul 25 2013, 5:29pm)