AWS Kinesis Streams is a scalable solution for real-time event processing, offering flexibility in data processing, subscription to Lambda functions, and integration with other AWS services like Firehose, Athena, and Analytics. It has no built-in auto-scaling mechanism but allows precise control over concurrency through the number of shards. DynamoDB Streams, on the other hand, is mainly used with Lambda, lacks direct integration with Kinesis Firehose or Analytics, and has limited data retention options compared to Kinesis Streams. However, DynamoDB Streams offers a more straightforward approach to removing distributed transactions from systems by separating responsibilities into multiple functions and using it instead of publishing to another Kinesis stream.