Is there really much of a difference between Fluro  compared to copolymer? I plan to use it on my Chatterbait rod.

For moving baits save the money and run copolymer or mono. 

Yes, there is a difference and there is a difference between different labels for both types of line.  What works best for you depends on your budget and what benefit you see using one over the other.

Personally, I only use fluorocarbon for treble hook baits, with the exception of topwater.  Less bow in the line during the retrieve, more sensitivity, less stretch (for the line I use) and better abrasion resistance are my reasons.  I don't like fluorocarbon for single hook presentation with the exception of finesse.  In the end, use what you have the most confidence in. One suggestion; Whatever type of line you decide on, get quality. It costs more, but when that hawg is on the other end, the last thing on your mind should be a concern over the line.