That's a somewhat misleading statement. Our strength of schedule was 11 and Vandy's was 54. But the difference between 11 and 54 is not a lot according to Sagarin. Vanderbilt's SOS was 70.25 rating but ours was only 76.94. So, even though there was a lot of difference in ranking there was not a lot of difference in the math. That means there were a lot of teams with pretty tough schedules through about the top 60 teams. And, all of the SEC teams were in that top 60. My point is it wasn't a whole lot harder. They beat both Georgia and Florida and beat us and we beat South Carolina and they didn't but played at Carolina. They will probably end up 9-4 and us 5-7. Does the strength of schedule justify 4 more wins? I don't think so.
I think the difference in SoS is greater than those numbers show. Here are a few random observations of Franklin's three year tenure at Vandy, and compare that to your knowledge of UT's past three years.
Here is a summary (cut and pasted from another post of mine):
In three years, the teams that Vandy has beaten
average a 4-8 record. 6 of the 23 individual victories of Vandy's came against teams who were so bad that the HC was replaced (that's almost 1 out of every 4 teams they beat). Vandy has only beaten 4 teams in three years who were bowl eligible (17% of their victories -or- two whole games less than the number of teams that were so bad that their coach was fired). Vandy, under Franklin, has never beaten a team that finished the regular season with more than 8 wins. The one time they have beaten a team with 8 regular season wins was this year against UGA. UGA's whole offense was basically benched for that game due to injuries.
This year UT's western division games came against Auburn and Bama ( two of the most talented teams in the SEC with a combined 2 losses between them) to Vandy's western division games (9 losses between them, both mid pack talent wise). Looking at the numbers, I believe firmly that UT goes 1-1 against Vandy's SEC west competition, accounting for 1 of the four game differences you described.
How about this: 10 of the 23 Vandy victories under Franklin came against teams with 3 wins or less.
Read that again, in three years, almost half of Vandy's miraculous wins came against teams who couldn't....win....4....games.
I think this removes any doubt that UT's schedule is exponentially harder over a series of seasons. The gap between the two teams insofar as SoS is much larger than you want to see. In fact, I think it is inarguable that if UT scheduled like Vandy (you know, not playing Oregon and instead schedules UMASS, or UAB, a WF - teams that totaled 7 wins this season), UT would also be going to a bowl (accounting for another of the win total difference).
While I don't believe that "intangibles" play a mathematically significant role in the outcome of football games, there is something to be said about the toll that a difficult schedule takes on a team emotionally and physically. Vandy avoids that punishment, UT hasn't. Is that physical and emotional toll enough to account for a 4 point swing in the outcome of one late season game? Perhaps that could account for one game in the win loss totals?
General Neyland thought so, as he famously scheduled "breathers" to make sure that his team only played a few tough games throughout a season. Those tougher games were to be separated by enough easier games to allow his teams to recover. He took much criticism for that tactic, and arguably that kept some of his UT teams out of the national title discussion on more than one occasion.
tl;dr
Scheduling and related events could account for a 3-4 game difference in win totals between Vandy and UT, as well as potentially changing the outcome of the UT v. Vandy head-to-head.