I don't know that we can really say that Gandalf was much more pure than other Maiar, there were a lot of Maiar and we only encounter a few of them in the legendarium. If we stay with the Istari we can ask: Why did Gandalf succeed in his mission where the other Wizards failed (or mostly failed)?
Well, Saruman fell due to his pride and jealousy, arrogantly thinking that no one else was qualified to deal with Sauron and the Ring. Radagast became distracted by his love for the beasts and birds of Middle-earth and lost his focus on his greater misison. The Blue Wizards might have been destroyed or may have given in to the corruption of power. Alternately, they might have succeeded in part, hindering Sauron's efforts to solidify his power in the East (and South?) even though they failed to identify where he was headquartered when he did not dwell in Barad-dur.