Amazon Web Services provides two main managed database services: Amazon Relational Database Service (RDS) and Amazon DynamoDB. RDS offers cost-efficient and scalable relational database capabilities for SQL databases, while DynamoDB is a NoSQL database optimized for fast performance. Customers should evaluate their data requirements such as structure, size, and access patterns to determine which service is best for their needs. Both services manage the administrative tasks of databases and provide resilient architectures with features like backups and read replicas.