The biggest difference between the sections is description. MORE STUFF DOESN'T "HAPPEN" IN "HIGHER" RPS. 

You're in a response cycle, which means you have to rely on other people to continue forward and progress. No matter the RP, there is a sort of indeterminate limit where you can't continue any further in your post without stepping on someone else's toes. The difference between sections lies in there. Free will cut all the fat and maybe leave one or two lines of motivations or descriptions. Advanced will give intricate reasonings for actions and details about the scene. Casual will be somewhere in between.

However, the key thing they share is that one person is acting, and there's only so much one person can do. It's why, in general, Advanced is slower than Casual, and Casual is slower than Free - there's less stuff to write, so each rotation of the cycle moves faster the less there is per post.