AWS X-Ray is a cost-effective distributed tracing solution that provides basic observability features, but has limitations such as requiring manual instrumentation in application code and poor support for event-driven applications. In contrast, Lumigo offers a more complete solution with automatic instrumentation, automatic error capture and aggregation, issues tracking through Jira, built-in alerting and notification, and high-level performance summaries for all Lambda functions. Lumigo also captures request and response bodies in HTTP requests, provides free-text search on collected data, and has better support for event-driven applications. While X-Ray is suitable for simple use cases, Lumigo stands out as the best observability tool for serverless applications due to its value proposition and features that cater to complex application needs.