From http://confluence.atlassian.com/display/JIRASTUDIO/Administering+Builds

Please note, the 'Admin' permission for standalone Bamboo has been renamed 'Restricted Admin' for Bamboo in JIRA Studio. The permission is essentially the same, i.e. grants access to 'Builds' administration, permission to delete plans and access to plan permissions for every plan.

We don't seem to document this anywhere in BAMBOO documentation.