Theories of equality of opportunity disagree about which factors affecting life chances are considered unjust. We distinguish between liberal inequality of opportunity, which considers the impact of ascribed characteristics such as gender, immigrant background, and social origin on life chances to be unjust, and radical inequality of opportunity, which additionally considers the effects of skills on life chances to be unjust, on the grounds that skills are themselves shaped by circumstances beyond individual control. Using data from 25 countries in the 2022/23 PIAAC survey, we test whether liberal inequality of opportunity, measured as the variance explained by ascribed characteristics, varies more across countries than radical inequality of opportunity, measured as the variance explained by ascribed characteristics and skills. We further test whether either conception is associated with a country’s level of income inequality, a relationship known as the Great Gatsby Curve (GGC). Contrary to our expectations, radical inequality of opportunity varies more across countries than liberal inequality of opportunity, and neither conception is associated with income inequality. These results indicate that the cross-national picture of inequality of opportunity depends on the conception adopted, and that the GGC holds for neither conception in our data.