Hyperpartisan news sources increasingly shape online discourse, raising urgent concerns about polarization and misinformation. This paper presents the first large-scale differential study of sentiment-driven engagement with hyperpartisan and non-hyperpartisan news on X (formerly Twitter). Analyzing 5.8 million news tweets that attracted 78.6 billion views (impressions) and 466 million interactions, we normalize interactions by view count to isolate user responsiveness, advancing beyond prior work that did not account for differences in exposure. Recognizing that the X algorithm tends to expose hyperpartisan users to hyperpartisan content more frequently, we provide insights into both what sentiments may make some publishers more successful and, more importantly, what effect those different sentiments have on these users’ engagement patterns at a large scale. Our findings show that hyperpartisan users exhibit greater sensitivity to negative content, a pattern robust to controls for topic, content prominence, and temporal variations, and consistent across left- and right-leaning hyperpartisan groups, despite subtle differences. Moreover, our analysis shows that the impact of sentiment on engagement is moderated by the depth of user cognition, varying across different interaction types such as likes, retweets, replies, and quotes. Our findings offer statistically grounded and actionable insights for content creators, recommender-system designers, and policymakers seeking to understand and curb the amplification of hyperpartisan content.