I lived in Phoenix for several years and now live just outside of Baton Rouge. They really aren't that different as far as cities are concerned. Pros and cons of either. If you're from a small town in Arizona, you may not like the lack of accessible land here
The crime is no worse than Phoenix and the people are about the same. It's about what you would expect, more Hispanics in Arizona and more Blacks in Louisiana. I treat all people the same so there's no real difference to me.
When I lived in Phoenix(really Cave Creek), it was easier to go out into the desert to walk around and sometimes hunt. It may not be like that today or it might not really be your thing but I liked doing it.
Hurricanes aren't really a problem in BR. Neither is flooding unless something unusual happens or you're in a bad spot
Hunting is a land use issue and I have no idea what you want to hunt or how aggressively you want to pursue it.
I originally wanted to live in a rural part of Mississippi just for the hunting but things didn't go as planned
Where you live in BR will make all the difference. You said it's a state job? Where at in BR?. I assume you would want to live somewhat close to work. This will make a big difference in how you like BR
Personally, I would want to be on the North side or Northwest side