Jules recognizes that Ringo isn’t a truly bad person at the core: he doesn’t want to hurt people (as mentioned in Ringo’s speech), he loves his girlfriend, etc. He is weak, and takes the easy way out by robbing people, but doesn’t want to actually hurt people.
But that’s not the life that Jules has led. He hasn’t tried to avoid hurting people…he has killed many people and thought nothing of it. Jules has come to realize that he has led the truly evil life. But he wants to change. He knows it won’t be as easy as just saying it. (“Now, I’d like that. But that shit ain’t the truth.”)
He has to live it. And he starts by showing compassion, restraint, and mercy by not only letting Ringo live, but by letting him keep the money…giving him a lesson not of strength, but of generosity.