Empowerment-based approaches to social development has attracted substantial attention in the last two decades. At the core of this debate is the preposition that empowering marginalised groups can improve their agency, with possible favourable implications for their life outcomes. The household bargaining literature has examined the effect of women's empowerment/bargaining power on development outcomes (e.g. health, education, agriculture and household expenditure). A core issue in this literature is the measurement of what constitute women's empowerment. The literature in economics and human development has tended to rely on the use of proxies that capture women's access to resources and or capabilities/functioning. This approach tends to ignore or deemphasise the importance of social norms/informal institutions (norms, values, traditions, beliefs etc), which via patriarchal gender stereotypes, restrict women's voice and access to resources. Although some researchers in demography have used proxies that capture social norms, they have been used alone, thus telling a single sided story as in the case of the economics and human development literature. Secondly, the discussion on the instrumental importance of women's empowerment in this literature seem to have focused mainly on mean development outcomes compared to the distributions of such outcomes in the population (inequality). Thus, the current study, using Demographic and Health Survey (DHS) data from 20 Sub-Saharan African (SSA) countries, computes a composite women's empowerment Index (CWEI), together with two sub-indices (social norms and access to resources) representing two dimensions of CWEI. The study further examines the comparative effect of social norms and women's access to resources on household health (i.e. mean health outcomes for women and children and poor child health inequality). Results suggest that in general, women from Southern Africa have a higher score on CWEI compared to their counterparts from East and Central Africa and West Africa. In addition, Southern African women are more able to negotiate social norms that constrain their voice and agency, whiles women from West Africa perform better on the access to resources index. Information from the DHS data and other external data sources (World Development Indicators database, International Labour Office and WEIGO), together with the SSA literature on the politics of liberation struggles and the formal/informal dichotomy of SSA economies, suggest that the sub-regional differences may be due to the unique history of liberation struggles in Southern Africa and the relatively large size of the informal sector in West Africa. Multivariate results also confirm the long held view that women's empowerment positively influences household health (mean health outcomes and inequality), with social norms having a much higher effect on household health compared to women's access to resources. In addition, the results suggest that other factors such as women's education, household wealth, access to and availability of health services, rural/urban and provincial differences have a higher effect on household health compared to the two dimensions of women's empowerment. The study concludes, advocating that interventions aimed at improving women's empowerment and bargaining emphasise issues of social norms, since they are likely to constrain women's voice, access to resources and consequently implications on household outcomes. This emphasis must however take into consideration the importance of other equally important factors (women's education, household wealth, access to and availability of health services etc), given that women's empowerment (especially informal institutions such as social norms) could take a long time to change and their effect realized in the long-term.