In chapter 4 How did One Eye show his greater experience and wisdom after the battle?

After the first battle with the three-year old? He made sure that he vanquished the leader as well; he saw his opportunity and he took it. This was experience, not physical prowess.

"But the elder leader was wise, very wise, in love even as in battle. The younger leader turned his head to lick a wound on his shoulder. The curve of his neck was turned toward his rival. With his one eye the elder saw the opportunity. He darted in low and closed with his fangs. It was a long, ripping slash, and deep as well. His teeth, in passing, burst the wall of the great vein of the throat. Then he leaped clear."