This study investigates how interface differences affect willingness for social sharing of emotion with conversational AI depending on motives (cognitive support vs. social-affective support vs. capitalization), while comparing social sharing of emotion with humans. Perceived impressions (warmth and competence) are examined as correlates of willingness ratings. Data from 195 Japanese undergraduates were analyzed. The results showed that for social-affective and cognitive support motives, participants preferred text-based modality over voice-based modality, particularly text-based modality without an avatar. For the capitalization motive, participants preferred interfaces with avatars. Moreover, perceived warmth was positively related to willingness for social sharing with AI for social-affective support and capitalization motives, whereas perceived competence was positively related for cognitive and social-affective support motives. A different pattern of results was found for social sharing of emotions with humans. This study provides novel insights that contribute to the design of conversational AI interfaces.