The picture I have is not that Thomas and Grant disliked each other at first, but that their staffs saw them as rivals, and the insults started lower and worked their way up to the top. (Gee, nothing like that could happen NOW) So, by the end of the Chattanooga campaign, Grant disliked Thomas especially after he had just won Grant the battle after Sherman had failed. I think the other problem might have been the mutual resentment felt between two men, one who had been allowed to resign to avoid charges for conduct unbecoming , and the other man well in the old-boy network of 2nd Cavalry. IIRC every officer in that unit went South-- with the exception of Thomas!
and yes, sometimes I feel sorry for Bragg.Of course, his bad moods brought it on himself; I remember one sketch of Bragg that ended with the words "and he died the singularly appropriate death of distemper." I've never been part of a formal hierarchical organization (except in theory) but I can well imagine what kind of Hell a man of Bragg's personality could make for his subordinates.