Chakotay's big disagreements with Janeway were when she was acting contrary to Starfleet Values.You're right, their closeness on Voyager was partially due to their friendship of 20 years but it didn't prevent Janeway & Tuvok from having disagreements from time to time. But contrary to Chakotay who was rather "brutal" in his opposition not systematic but regular (honestly, if his Maquis crew had been larger, I'm pretty sure that Chakotay wouldn't have hesitated to throw a mutiny), Tuvok knew how to confront her friend with her contradictions and/or to advise her without antagonizing her in her cuttings off. -> I'd say that Tuvok was the voice of reason of Janeway and because of that, she listened to him more closely (besides, even Chakotay recognized Tuvok's great influence on Janeway and we saw that when Tuvok was in bad posture, he turned irrevocably to Janeway for a physical, moral or intellectual support -> they understand as nobody and that's what is great.
If I remember well, Chakotay's disagreement with Janeway were often due to what they were: Janeway thought as a Starfleet commanding officer while Chakotay thought as a Maquis commanding officer (although, himself a former Starfleet officer but I guess that since, he rejected Starfleet's policy & rules) and althought he wore the Starfleet unifom, he didn't stop thinking and acting as a Maquis throughout the journey (he was lucky that Janeway let him acting like that!). Result: 1 given situation, 2 points of view diametrically opposite to respond (and same thing for the tools used, of course).
-> whether it was Cuvit or Tuvok, the disagreements with Janeway would have settled in Starfleet style : cf Kirk/Spock; Picard/Riker : no direct confrontation. the XO suggest without trying to impose his will, what Chakotay tried too often to make a passage in force with inconvenient results.
-> if Chakotay was angry with Janeway's behaviour in Equinox, I wonder how he would have react with Sisko, who, when he had an objectivein mind, went to the end and no matter the consequences. Both would certainly have come to hands to resolve the conflicting situation and it isn't sure that the winner would have been Chakotay, in spite of his experience of boxer.![]()
-She wants to take sides in War. The side she chooses is the Borg! Chakotay objects, because he shares Starfleets values. He was a career officer, and even as a Maquis, he is still a Federation citizen.
-Janeway has a Vendetta with Ransom. Chakotay doesn't like it. Janeway later attempts to torture(or threaten torture) one of Ransom's crew. For Chakotay, Janeway has completely crossed the line. He takes matters into his own hands. Janeway relieves him, but later admits she was wrong.
I can't see Chakotay ever supporting a guy like Eddington, who used his position at Starfleet dishonorably. Chakotay resigned peacefully (as far as we know) to go to the defense of his friends and neighbors, since Starfleet couldn't interfere.
And Sisko too. Chakotay would be disgusted by what he did during his own irrational vendetta.