A lot of people think the coral is happier hanging upside down because often you see them on the reef hanging upside down under caves or on cliff walls. Personally, I feel the reason for this is just because there are less corals to compete being as dendros, scleros, dendrophyliidae, etc. are non-photosynthetic, there are considerably less corals to compete with them due to being shaded. In tanks where many of these corals don't do all that well traditionally, hanging them upside down can sometimes help them to expand (or appear to expand) by letting gravity help out elongating them. Because the chilli coral doesn't expand like dendros or scleros, I doubt hanging will make any real difference in appearance or health.
Aaron