Georgia Southern is a fine regional state school. It serves Southeast Georgia well and attracts a large number of metro Atlanta students. I agree that the top students at a GSU would be successful students almost anywhere. Many top students will choose the highest academic scholarship at a school like GSU and the advantages that affords over attending a more renowned school where they are granted admission.
Tulane is a well-respected private university in New Orleans. It is going to have certain programs and graduate/professional schools that are much higher regarded than anything comparable at Georgia Southern. It could be argued that Tulane's academic reputation has plateaued or declined, particularly post-Katrina, while Georgia Southern is more on the rise. But, no one would seriously argue GSU is the better school academically.
As for football, Tulane has a long legacy that goes back to SEC days. They have been awful, for the most part, for five decades now. Only a couple of coaches have come to Tulane and moved on to better jobs in recent years. They have the new stadium, but any early enthusiasm seems to have faded. Their conference afford them few natural rivals. Success at Tulane will be hard to come by.
I think GSU fans are reasonable in believing Fritz is not making a move up the college football coaching ladder. Fan interest in Statesboro is high and the attractiveness he could have gained with another strong season or two would have led to a much better coaching gig than at Tulane.