Global analyses of urban greenspace have traditionally highlighted a North-South disparity, yet a critical gap remains in understanding how climatic and socioeconomic factors differentially drive greenspace exposure inequality across these regions. To address this, we introduce a novel Greenspace Exposure Inequity Index (GEII) and apply it to 1,370 cities worldwide. Our analysis reveals a more complex picture than the conventional divide: while cities in the Global South generally exhibit slightly higher inequality, those in arid regions of the Global North display greater inequity. Through a machine learning approach, we identify distinct primary drivers-the Human Development Index (HDI) dominates inequality in Global Northern cities, whereas GDP, greenspace coverage ratio (GCR), and total annual precipitation (TAP) are pivotal in the Global South. Crucially, we detect statistically significant nonlinear thresholds that act as tipping points in these relationships. Specifically, thresholds for GDP (natural-logarithm scale: 23.851) and TAP (1017.158 mm) are identified in the Global South, and for GCR (0.55) in the Global North. The identification of these thresholds provides actionable insights for urban planning: prioritizing human-centered development and equitable greening in the Global North, and optimizing greenspace planning coupled with water resource management in the Global South, to mitigate greenspace exposure inequality effectively.