I think you may be asking the wrong question. It is not really "who was the true hero" but "who do we learn from most?" You can argue that Frodo was a hero, because of his courageous choice and resolve. The same might be said about Sam, though his choice might have been less in order (he chose for the sake of his master, Frodo chose for the sake of the Shire/Middle Earth). However, when it comes down to it, Sam is the character you identify with, not Frodo. Frodo's role is tragic, because he does succumb in the end. By the time the ring was destroyed, the noble attitude that drove Frodo to make his choice was all but gone. The reader begins the story identifying with Frodo, but ends it identifying with Sam because he is more
human. Frodo became a broken, changed hobbit, who's only hope in the end lied in going West across the sea. Sam, however, has a relatively happy ending. He does the deed, gets the girl, and lives a good life. Therefore, we are naturally more drawn towards Sam. He is the character the average reader has the most in common with (ideally, anyways).
I suppose the best way to think about it is by looking at the emotion you experience at the end of the books towards each hobbit. Personally, I feel sympathy and pity for Frodo (because, like I said, he is a tragic figure). But I admire Sam for his basic qualities of loyalty and love. In the end, who would you want to be? I'm sure most people would say, without hesitation, "Sam".
Of course I know that all this isn't fair. Any comparison between the principle Ringbearer and another character can't be. The Ring's influence on Frodo is the cause of all his tragedy, after all. But in the end, my point remains the same. Samwise Gamgee is still the hobbit you relate to, and Frodo is the one you pity. At least that's how I feel
.