Throughout the episode "Reunion", Gowron at least makes an effort to cooperate with Worf, and even shows him courtesy, despite the fact that Worf is seen officially as a traitor to the Klingon Empire. Duras, on the other hand, outright insults Worf, mocks him, disrespectfully answers him. Even when Worf comes in to confirm the findings of the bombing which happens later in the episode, Gowron only says "he has no place here Picard," whereas Duras disrespectfully says "I will not sit in the same table as that". In the way they answer, Gowron answers with respect, but Duras answers with insulting mockery. Why?
Because Gowron can read the room better than Duras. Duras mainly inherited his station in life from his father Ja'rod; the House of Duras is a strong one and considered very mainstream in Klingon politics. On the other hand, Gowron was a relative outsider; Worf knew little of him, except that he'd often disagreed with the High Council. For a political outsider to come to lead one of the two biggest factions in Klingon politics implies a level of skill at reading and manipulating people that lets him build a powerbase up from scratch.
When confronted with Picard doing strange things as Arbiter of Succession, Gowron's instinct is political: try to avoid antagonizing him and making an enemy for no reason. Picard clearly is not going to let the two of them fight for succession in the usual way; he calls for the ja'chuq ritual to buy time and then springs the results of Worf's investigation on them. The obvious conclusion is that Picard is going to pin the bombing on one of the candidates and use that to disqualify him, thereby determining the next Chancellor. Gowron wants to be that Chancellor, so he's going to be, if not polite and likeable, at least more polite and likeable than Duras. He knows that Worf is heading the investigation and doesn't want to antagonize him; he knows that Picard is dangling Worf in front of the two candidates as bait and he doesn't want to be seen rising to it.
Remember the subtext of the Duras-Worf relationship: Worf accepted discommendation because, officially, the Klingon High Council has declared his father, Mogh, to be the traitor that betrayed the Khittomer outpost to the Romulans. In reality, it was Duras' father that was the traitor, but Duras was too powerful and trying to share that truth would have possibly sparked a civil war. From Sins of the Father
WORF: Why did you judge my father guilty when you knew he was not?
K'MPEC: Someone had to be blamed. The warriors who captured the Romulan ship had learned of the treachery, but only the Council knew whose security code had been transmitted. Ja'rod, father of Duras.
WORF: This ha'DIbaH should have been fed to the dogs!
K'MPEC: His family is powerful. If the truth were known, it would shatter the Council, most certainly plunge us into civil war. You were in Starfleet. We did not expect you to challenge the judgment, nor did we know there was another son of Mogh.
WORF: If you allow [my brother] to live, I will give you something that will serve your purpose far more than my death. I will accept discommendation.
DURAS: You would do this in open council?
K'MPEC: It would be the same as admitting your father's guilt, Worf.
WORF: So be it.
K'MPEC: Your heart is Klingon. It will be done. What has been said here will never be spoken of again.
WORF: You are the son of a traitor.
(Worf slaps Duras' face)
WORF: Now I am ready.
Gowron doesn't know this, only that Worf accepted this dishonor in front of the council, which is unusual for a traitor. Gowron would gain nothing from being belligerent to the officer of the Arbiter of Succession (Picard), so he merely keeps to the code in objecting to Worf's presence.
Duras was Gowron's rival for power. Gowron had no incentive to cooperate with Duras or to view him positively. Worf is a mere disreputable person, albeit in a culture where that is a pretty big deal; Duras is an actual enemy. Gowron had incentive to tolerate Worf simply to not go along with Duras.