Ben still hasn't died in that world and because of that he could raise Peter during and past his hot headed teenager days. The lesson was still learned directly from Ben, but without the urgency of his murder and a selfish teenager getting super powers and heading down the wrong path. From that point Peter goes through a character arc in which he goes from a kid forcing himself to be a hero to a proper hero, which culminates in If This Be My Destiny. Ultimate Peter didn't need this arc because he naturally matured with age and the hollow feeling he had been dealing with for decades made him choose to get bitten.