Alabama and Ole Miss have played only 53 times with Bama having won 42 and two having been tied, so the Rebels have only nine wins in the "rivalry." But it's also true that Alabama did not go up against many of the best Mississippi teams under Vaught, who coached 1947-70 and then a handful of games in 1973 when the Rebs booted Billy Kinard in mid-season.
In the 1950s, Southeastern Conference schools were not required to play a set number of SEC games. In some years, after the SEC required a minimum number of league games, teams sometimes would have "designated" conference games. If six SEC games were required and a team played only five SEC teams, a Southern Miss or someone like that was designated as a conference game.
In the 1960s the SEC took over scheduling of SEC games–that is SEC teams playing one another–and so their began to be some rotation so that, for instance, Alabama more often would play Florida, Ole Miss, Kentucky, and Georgia, teams Bama had not often played.
Alabama has played far more conference games than any other SEC school, 504. Florida has played the least, 455.
Just as an example, in 1954 Ole Miss won the SEC with a 5-1 SEC record. About half the league teams played six games that year. Some played seven. Georgia Tech, Alabama and Tulane played eight.
In 1980 and 1981 Alabama and Ole Miss played and the games did not count as SEC games. That was because Alabama had begun scheduling some of its open dates against SEC teams. In at least one year, 1972, Alabama won the SEC championship because it played (and won) one more conference game, having added Kentucky. But it worked against the Tide in 1976 when Alabama fell to Ole Miss in the season-opener in Jackson and finished with a 5-2 record while Georgia and Kentucky shared the SEC title with 5-1 records (the Wildcats' with an asterisk since it got a forfeit from Mississippi State a year or two later, courtesy of the NCAA).
Prior to the 1980 season, the SEC presidents voted that a game scheduled by two SEC teams against one another, but not scheduled by the conference office, would not count in SEC standings. They didn't want Alabama, which had won eight of the previous nine SEC championships, to have an advantage. Alabama and Mississippi were scheduled to play in 1980 and 1981, games the two schools worked out. Alabama won both the 1980 and 1981 games against the Rebels, but the games between the two charter SEC members did not count as league games.
The extra game wouldn't have helped Alabama in 1980 when Bama lost a controversial game to Mississippi State and Georgia went undefeated at 6-0. In 1981 Alabama and Georgia tied for the SEC title with official 6-0 records, although Bama had a seventh non-counting victory over the Rebels.
Paul Bryant won more SEC games in his 25-year tenure (1958-82) at Alabama than any other coach in league history. He was 137-28-5. Bryant also had a 22-18-4 record in SEC games while at Kentucky, 1946-53, giving him a total SEC record of 159-46-9. John Vaught ranks second in SEC coaching victories with his 106-41-10 mark in conference games.
The first Alabama-Bryant vs. Mississippi-Vaught meeting came in the Sugar Bowl at the end of the 1963 season, Alabama winning that game on the strength of Tim Davis' four field goals, 12-7. The Tide and Rebels played in regular season games the next seven years with Alabama winning five times. The most memorable in that group was the 1969 battle between Bama's Scott Hunter and the Rebels' Archie Manning, Alabama winning by 33-32.
So it was Alabama-Bryant with six wins, Ole Miss-Vaught with two.