I think answer should be Log Analytics
What kind of telemetry data is being handled by Log Analytics ? -> Data related to infrastructure and network level i.e., few of them are syslogs, IIS logs, custom logs, windows events, windows and linux performance counters, etc. For more information, please refer https://docs.microsoft.com/en-us/azure/azure-monitor/azure-monitor-log-hub
What kind of telemetry data is being handled by App Insights ? -> Data related to code-level application performance level i.e., few of them are ping URL tests, page view counts, page view load data, HTTP requests, dependency calls, exceptions and stack traces, custom events and metrics that you code, trace logs, AJAX calls, user and session counts, run-time exceptions, failure anomalies, abnormal rise in exceptions, etc. For more information, please refer https://docs.microsoft.com/en-us/azure/azure-monitor/azure-monitor-app-hub and https://docs.microsoft.com/en-us/azure/azure-monitor/app/troubleshoot-faq#what-telemetry-is-collected-by-application-insights