Urban Dictionary defines "second city syndrome":
When a smaller city talks down on a larger city due to insecurity of its own size and/or having less culture, music, art, employment. Usually this happens between two cities that are relatively close to one another.
Some great West Coast examples are Portland and Seattle, Los Angeles and San Francisco.
I would add Phoenix and Tucson.
Having lived in both cities, I've noticed the extent to which Tucsonans regard Phoenix as the urban sprawl to the North, a bastion of ultra-conservative fanatics, a collection of growth maniacs and money-hungry barbarians, etc.
Phoenicians, on the other hand, rarely think of Tucson at all. Many Phoenicians went to the University of Arizona and have fond memories of their student days. In my north Phoenix neighborhood, I often see U of A flags and insignia.
I've yet to see any equivalent Arizona State University loyalties displayed in Tucson. Doing so would be regarded as a form of treason.
Is a second city syndrome present in your state?