In Webster's Dictionary, a hero is defined as a person noted for courageous acts or nobility of purpose, especially if this individual has risked or sacrificed his life. It can also be used in reference to a mythological or legendary figure, often of divine ancestry, who is favored by the gods, endowed with great courage and strength, and celebrated for his bold exploits. War or dangerous adventure is the hero's normal occupation.
In my opinion, Odysseus is much more heroic than Achilles. Throughout both the Iliad and the Odyssey, Odysseus showed more cunning and acts of bravery than Achilles. Both men did make an attempt to avoid fighting in the Trojan War, however, neither succeeded. After Odysseus was tricked into serving the Greeks, he was sent to recruit Achilles. Disguised as a peddler, he approached Achilles, who was dressed as a woman hiding among the maidens, and displayed trinkets and fine weapons. "While the girls flocked around the trinkets, Achilles fingered the swords and daggers." After Odysseus discovered him, he persuaded Achilles into coming to the Greek camp and joining their army. This shows that Odysseus was smarter and cleverer than Achilles. Odysseus also showed cunning when he came up with the plot to defeat Troy, using the Trojan Horse.
Odysseus fought bravely throughout the entire Trojan War, whereas Achilles spent quite awhile in his tent pouting after Agamemnon kidnapped his prize maiden, Chryseis. He also lets his best friend, Patroclus, go into battle alone to die by Hector's spear. It takes a great loss like this for Achilles to get up and fight again. Even then he was not fighting out of bravery, but purely out of anger, with the desire of revenge. Then, after Achilles had killed Hector, he fastened Hector's feet to his chariot and drug his body around the walls of Troy. This act was disturbing and definitely not that of a hero.
Even after the Trojan War was over, Odysseus had to go through twenty years of turmoil before he could get home. He endured all of this with the hope that someday he would again be with his family. I thought that this was very honorable.
I would definitely consider Odysseus a greater hero than Achilles. He was smarter and much nobler. He showed nobility by tricking Achilles, fighting bravely, and enduring many hardships to get back to his family. A hero is one who exhibits courage and honor. It is a person who puts the interest of others ahead of their own. This is what a hero is and if we all lived by this code of honor, then I think that the world would be a much better place.