Difference between "empathetic" and "empathic"
For better or worse, the meaning of the word empathic has been forever tainted by its use in the science fiction and fantasy realm -- I would avoid using it interchangeably with empathetic just to avoid the connotation of spooky action at a distance. "Correct" and "right" aren't interchangeable either -- using language correctly isn't right if it raises unnecessary misunderstanding.
An empath is a person who reads the emotions of those in the vicinity, so logically empathic implies a connection to an empath. Empathetic is more like the tendency of someone to care for another in general. So where empathic seems to pertain to a person's ability to perceive emotion, empathetic is more like how others tend to sympathize with a person or situation.
So if you're referring to a writing, I would use "empathetic" unless you want to imply that it's something for which you personally feel emotion.
Merriam-Webster says:
empathetic, adj. : involving, characterized by, or based on empathy
empathic, adj. : empathetic
The Grammarist notes that empathetic is used about five times more often than empathic in news publications, "probably due to analogy with sympathetic."
Google Ngrams, however, shows empathic winning; Language Log speculates that this may be due to the prevalence of empathic in psychological research and, yes, science fiction.