The EBA and ESMA

The EBA and ESMA perform tasks associated with the proposition, analysis and release of new regulation affecting the banking and capital markets of Europe respectively.
ESMA was created to establish an EU-wide financial markets watchdog, who will create regulation to improve the functioning of financial markets in Europe, strengthening investor protection and co-operation between national competent authorities.

The EBA has the power to overrule national regulators if they fail to properly regulate their banks. The EBA will prevent a race to the bottom because banks established in jurisdictions with less regulation will no longer be at a competitive advantage compared to banks based in jurisdictions with more regulations as all banks will henceforth have to comply with the higher pan European standard. The EBA is mandated to assess risks and vulnerabilities in the EU banking sector through, in particular, regular risk assessment reports and pan-European stress tests.
The EBA develops draft BTS which are finally endorsed and adopted by the European Commission. Contrary to other documents such as guidelines or recommendations, the BTS (binding technical standards) are legally binding and directly applicable in all Member States.