This bickering is pointless...
Majors was a UT legend and helped rebuild the UT program upon his arrival in 1977. He played a ridiculously hard OOC schedule from 1978-1981 which slowed the rebuilding effort, but began to recruit both local UT stars, and elite NFL talent from out of state ALONG with putting together top notch assistant coaches. He did have an up and down year to year type program, but had top ten teams in 85, 87, 89, 90, 91, 92 along with three SEC titles and could've won NCs with a little less hard scheduling and a little more luck. He had some of the greatest wins in UT history but also got too conservative and lost some stinkers. He was an alcoholic but rightly complained about his salary in 1992 which was at the bottom of the SEC despite being so elite at the time. His rushing back from surgery and calling donors and the AD and some Board members drunk at 3am about his salary was his undoing, but it doesn't diminish his coaching ability or his status as UT legend.
Fulmer was a great UT player as well, and became an outstanding coach. He did help Majors firing happen, but he was a good coach overall. Tennessee was dominant in the 1990s and yes Spurrier's owning of him from 93-97 helped cement that narrative, he still beat Spurrier more than any other SEC coach by far. He continued the great elite NFL talent, but where he struggled was hiring top notch assistants after Cutcliffe left. He was stubborn and like to old school it a little too much, and had some stinker losses too, but the guy still won at a high clip against a really difficult schedule. His refusal to make changes was his undoing, and he created more serious problems as AD which wasn't for him, BUT he still was a great coach just like Majors.
These two were both two of our greatest HCs of all time in the sport, and while they do have faults, it's dumb to complain about them now or just focus on their shortcomings or who was better.