Understanding the Requirement: The data science team needs to securely share selective data with the engineering team across multiple AWS accounts with minimal operational overhead.

Analysis of Options:

Copy data to a common account: Involves data duplication and increased storage costs, and requires managing additional permissions.

Lake Formation permissions Grant command: This method can be effective but may involve significant operational overhead if managing permissions across multiple accounts and datasets manually.

AWS Data Exchange: Designed for sharing data externally or between organizations, which adds unnecessary complexity for internal sharing within the same organization.

Lake Formation tag-based access control: Provides a scalable and efficient way to manage access permissions based on tags, allowing fine-grained control and simplified management across accounts.

Best Solution:

Lake Formation tag-based access control: This solution meets the requirements with the least operational overhead, allowing efficient management of cross-account permissions and secure data sharing.