The way I see it, and I may be way off, is Majors and staff were good coaches. They elevated a TN program that Battle had kind of sent on a downward trajectory. Fulmer and company were competent , but really won mostly on raw talent and recruiting stability that had been established already. Spurrier saw through that and figured if he could provoke an arrogant Fulmer into playing more aggressively , his quick passing game would take advantage of us early on and put us into playing catch up and be out of our comfort zone. The well coached teams with high level talent could handle all that jazz that Spurrier did, but we just never could. We were always out flanked and a step behind. I don't think he'd ever have anything much to say about BJ ,because Jones inherited a true mess and there's not much you could say negatively about him if he turns it around.
I largely agree but with a few caveats. Majors had a knack for hiring excellent assistant coaches who went on to greater success elsewhere. He was, by his own admission, a "tough/mean SOB to work for." On the other hand, the very best Majors-coached teams were, as you noted, when a measure of stability and upward momentum had already been established and in years when Fulmer held greatest responsibility as an assistant coach. For example, check out the productivity of our offense when Fulmer was offensive coordinator. Admittedly, Shuler was quarterback but they were some of the most explosive and highest-scoring offenses we have ever put on the field. Conversely, Fulmer elevated Tennessee to an absolute recruiting juggernaut during the first half of his tenure; this was most apparent on the defensive line, where, for once, we actually stockpiled elite talent, even at tackle.
With respect to Spurrier, Florida was most dominating during Danny Wuerffel's tenure; Wuerffel was a perfect match for Spurrier's offensive system. After his departure, Florida remained a formidable adversary but not one that was virtually invincible. I am inclined to agree that, while Peyton was there, perhaps Fulmer and Cutcliffe were willing to engage Spurrier and his charges in a firefight. We are all familiar with the net result of that approach.
For the following hypothesis, I have no links, no quotes and no documentation but it is my considered opinion that Fulmer, Cutcliffe and Chavis retooled their collective gameplan and came up with a strategy that gave us a better chance for victory: Avoid the temptation of engaging Spurrier in a shootout, run the football more, bleed the clock and limit Florida's offensive possessions. I believe the evidence is there if you compare the outcome of games played between 1994-1997 and 1998-2001, respectively. During the first four games, Florida either won by large margins or amassed large leads only to surrender large numbers of late cosmetic points prior to the inevitable victory. During the last four years, Tennessee and Florida split 2-2 and no game was won by more than 4 points. Overall scoring was lower in those games as well. Predictably, Tennessee ran the ball most effectively in their two victories (1998 and 2001).