With Ulysses on the Greeks side they had amazing intelligence and bravery. Many great things happened because of Ulysses leadership. One example is when Ulysses dressed as a peddler, found where Achilles was hiding, and brought him back to fight in the war. Ulysses knew he had to find Achilles because the prophecies told the Greeks they couldn't win the war without him. Secondly, Ulysses convinced the Greek forces to return and fight after Agamemnon almost lost them. He yelled to the troops "Stop! Agamemnon means battle and not retreat, you misunderstood his words" (p. 42). Lastly, Ulysses showed great smartness when he solved the riddle about the Trojan War. By him solving the riddle, the Greeks came to win the long war. Ulysses was also smart enough to think of hollowing out the horse so the Greeks could hide inside them and attack the Trojans while they were sleeping. He showed intelligence too when he pretended the horse was a sacrifice to the god Poseidon. The war may not have turned out the same if the Greeks did not have the great leader Ulysses.
While Ulysses was using good and honest traits to keep the troops in line, and to win the war, Agamemnon was causing many problems. His stupidity and arrogance made him unfit for leadership. An example of him being selfish is when he sacrificed his own daughter, Iphegehia, to the gods so he would have good luck and a safe journey to and from Troy. When Agamemnon returned home from the war his wife killed him for sacrificing their lovely daughter. A time showing Agamemnon as ignorant was when he almost lost all of the troops. He told them it was time to leave the war and head home. He was only trying to weed out the cowards, but it turned out everyone ran for the ships. Thirdly, he refused to give back Cressida, his slave girl, when he was supposed to. As a result, Apollo shot arrows of pestilence at the Greeks. Many Greeks ended up being killed. Lastly, he was selfish and took Achilles slave girl when his had to be returned. He said, "It is my duty to take someone else's slave to repay me for the loss of the lovely Cressida, for a king deprived is a half a king, and half a king means defeat in warfare" (p 29).
As you can see Ulysses is a brave, smart man who helped lead the Greeks to a tremendous victory. On the other hand, Agamemnon caused suffering and pain for not only individuals but for all the men fighting. Some believe that if the Greek troops had not been led by Agamemnon the war would not have lasted as long. Maybe that statement would be true, maybe not, but we all know that in the end Ulysses brains on solving that riddle was the reason the Greeks had won the war.