Joomla privacy plugin is mostly meant for capturing consent, allowing user export, allowing user delete, and user action log.
CB Privacy provides privacy controls for users tabs and fields, allows user export, and allows user delete. CBs captures consent already as part of its terms and conditions field; you can turn on verify consent within CBs system plugin. For a user action log you can use CB Profile Update Logger.
It's not recommended to use Joomlas and CBs privacy features at the same time, but you can if you want.