Answer and explanation:
Yeats' statement that the best lack all conviction while the worst are full of passionate intensity applies to the speakers of both poems because the two of them are good people who lack all conviction.
We can conclude the Irish airman is a good, ethical person, since his decision to fight for his country is the "right one". It is what everyone would expect of a decent man. However, the Irish airman himself is not convinced of his reasons to do so. He does not believe his cause is fair. He knows there are good people among the enemy and bad people in his country. He is not driven by conviction that his actions are good, right, necessary. As he says,
Nor law, nor duty bade me fight,
Nor public men, nor cheering crowds,
A lonely impulse of delight
Drove to this tumult in the clouds;
Prufrock, the other speaker we are analyzing here, is also a good person who lacks courage, conviction, beliefs. He is a sensitive man with a heightened ability for observation. He desires human contact and interaction. He wants to be loved, to receive attention. However, he is deeply afraid of society's criticism, and ends up isolating himself before anyone else has the chance to do it. His lack of courage and self-esteem does not allow him to enjoy life.
No! I am not Prince Hamlet, nor was meant to be;
Am an attendant lord, one that will do
To swell a progress, start a scene or two,
Advise the prince; no doubt, an easy tool,
Deferential, glad to be of use,
Politic, cautious, and meticulous;
Full of high sentence, but a bit obtuse;
At times, indeed, almost ridiculous—
Almost, at times, the Fool.