This paper explores the concept, measurement, principal stylized facts, and normative implications of compositional inequality. Compositional inequality refers to how the shares of capital and labor income vary along the income distribution. This analysis is valuable for several reasons. From a macroeconomic perspective, it elucidates the link between functional and personal distributions of income, which is crucial for addressing the drivers of income inequality in a context of AI-driven, technology-augmenting capital accumulation. From a comparative economic perspective, it locates economic systems on the continuum between two extremes: classical capitalism, where the rich earn predominantly from capital and the poor from labor, and new capitalism, where the composition of capital and labor is uniform across the distribution. We refer to the entire range of systems along this continuum as the distributional varieties of capitalism. Recent empirical studies indicate that, in most countries, we are far from classical capitalism, though with notable exceptions, such as Latin American countries. This underscores the need to evaluate the benefits of compositional equality. The paper concludes that compositional equality is desirable for at least two reasons: it promotes fairness and supports an inclusive, profit-driven regime of accumulation and growth. (Stone Center on Socio-Economic Inequality Working Paper)