Interesting takes on the scene with Picard and Sisko. In my view, Picard and Sisko are completely different men. Picard is both reserved and self aware. Sisko is hot headed, angry and not yet self aware.
Picard had been completely assimilated, he was acting as the voice or the liason for the borg--- it was not Picard who was attacking federation ships, it was the borg. If Picard was killed, the cube would have continued on to sector 001. Picard underwent counseling and he had feelings of guilt and horror of being striped of humanity and being used as tool against all that he loved. But he continued on with his job, not wearing it on his sleeve.
Sisko on the other hand is not quite as aware, he is still working on things and has not dealt with his tragedy. He seems to blame Picard...which is similar to a person who is angry at someone for getting a disease because it adversely affects them. When a person gains some wisdom, they recognize the sick person is suffering, and the anger that is misdirected at the victim disappears. Sisko has an experience in the worm hole that opens his eyes, and he realizes he is not seeing full reality. He is living in the past. He was stuck, not seeing things as they really are: His wife is gone forever and he must continue with life, and Picard was a victim too.
I don't think Picard was rude to Sisko. When Sisko was disrespectful, instead of lashing back, Picard clearly hears Sisko's pain, and he just lets it be said, you can see it register in Picard's head- he understands Sisko's pain. Because of his own feelings of guilt, Picard excepts Sisko's rudeness as understandable. When Sisko continues with his angry tone, and clearly states he dos not want the position, it makes sense for Picard to bring up the idea of replacement.
Becasue Sisko was living in the past, and focusing on blame, he could not really live. By focusing on blame, it kept his mind away from the deepest pain (his wife is gone forever and he has to leave her behind and live). He got stuck, growth stopped...until he entered the wormhole.