After decades of global trade liberalization and the enthusiastic establishment of global supply chains for reasons of cost efficiency, market access and expected opportunities for upgrading, the negative social and environmental impacts of global supply chains have received increased attention. In recent years, a swathe of public supply chain-related legislation has been adopted in different, mainly European, countries, possibly replacing the hitherto dominant yet largely unsuccessful private sustainability governance regimes. Given the novelty of due diligence approaches, it is unclear to what extent and in which ways the due diligence ‘logic’ actually changes the ways in which MNCs as well as the public and civil society actors holding them accountable address social and environmental risks and responsibilities in global supply chains. In this paper, we draw on interview, document and observation data among various stakeholders in Germany and on an EU level to examine the enactment of two recent examples of human rights due diligence legislation: the German Supply Chain Act, in effect since January 2023, and the EU Corporate Sustainability Due Diligence Directive (CSDDD), negotiated in 2023-24. We identify five tensions accompanying the implementation of these legislations, which suggest that the shift from market-based enforcement to legal enforcement may be more gradual than anticipated, and that the distinction between the enforcement mechanisms of private and public regulation might be less clear and drastic than usually expected. Practically, this stresses the need for a mix of modes of governance where civil-society contestation should by layered onto public/legal enforcement.