If you are interested in a real answer, I'll try to give it to you.

Both Ole Miss and Mississippi State had good 10-15 year runs before the 60s. Ole Miss was with Vaught, MSU was pre-World War II. So I am assuming you are referring to modern college football.

Here are the factors.

1. Degegregation hit the Mississippi schools harder. It took a few years after the Mississippi schools allowed black players for black players to even want to go to State and Ole Miss. As was mentioned, Jerry Rice (who grew up right outside Starkville) and Walter Payton went to HBCUs. "The best that never was," Marcus Dupree only considered Southern Miss in-state. This was the 1980s, 20 years after black players were allowed.

2. A reluctance to build a student-centric atmosphere. Its no secret that State and Ole Miss played the Egg Bowl in Jackson for many years, but most people don't know that State and Ole Miss played most of their SEC home games in Jackson for 30 years. Bigger stadium, closer to alumni base, etc. - but it killed the on campus atmosphere of alumni coming in and students going to games. From 1977-1981, things were so bad that MSU played no more than two games on campus in a season, and in four years, only faced one team with a winning record on campus.

3. This led to another problem. Facilities were awful. In the 1980s, the first boom of college football facility wars were starting. Because the Mississippi schools barely played on campus, no improvements were made. In 1995, the Mississippi schools' on campus facilities held about 40,000.

4. A series of bad coaches. Partly because of the good old boy system, and partly because of the lack of finances, both Ole Miss and State went through a period of years where the coaches were not SEC-quality. Bob Tyler was 21-44 at MSU in the 70s. Rockey Felker was his QB. They hired a 33 year old Rockey Felker in the 80s. He went 21-34. Steve Sloan killed what Johnny Vaught built at Ole Miss.

5. The horrible education system in Mississippi. A novel could be written about the mistakes here, but Mississippi has a good share of football talent. As recently as 2004, most of the Dandy Dozen were not academically eligible. Mississippi has JUCO football, and the JUCOs are happy to take these academic casualties, but it has always been used as a fall back. For years, Mississippi was the only SEC state that had junior college football, and it hurt State and Ole Miss under the guise of helping them.