The term empathetic appears to be the one commonly used in experimental psychology, social neuroscience, and cognitive science. Perhaps because empathic may have been preempted by clinical psychology as well as popular psychology, often with a special emphasis on picking up another’s moods and feelings. It is also used to characterize people who are especially good at such things. In contrast, empathetic would typically cover a variety of responses and capacities, unconscious as well as conscious, involved in the perception of other people. These include the ordinary everyday capacity to interpret another’s behavior unconsciously by internally mirroring it (via mirror neurons).

So, independently of StarTrek, I come around to agree with Maeve’s suggestion:

I would use empathetic to describe the empathy an ordinary person feels. I’d use empathic to describe the feeling experienced by an empath.

The Ancient Greek dictionary I just checked lists:
a) someone who has lost self-control & is overtly emotional/shaken
b) “εμπαθής τινί”/ “εμπαθής προς τι” (empathetic towards something): someone excessively affected by something
c) “εμπαθης φιλία” (empathetic friendship): very passionate friendship

Excuse the bad translation (i really need to get to sleep), but isn’t it interesting how the Greek & Ancient Greek uses are so far apart and how the English is actually closer (but not identical) to the Ancient Greek? The obviously all revolve around the idea of passion (one of the meanings of ancient & modern greek πάθος [pathos]) but the Modern is VERY negative. ho-hum.