The Basel Committee spent most of the decade before the crisis dominantly focused on the Basel II framework, which was intended to reduce somewhat effective regulatory capital levels for large banks in return for their transition to an internal-models-based approach to capital requirements.
This was a choice made by national regulators, led by those in the United States, and not a byproduct of the structure of the Basel Committee itself. Adding the lessons of the 2007–09 financial crisis to those of earlier episodes of financial stress, I think we can infer some guidelines on host and home responsibilities to help shape expectations for practice.