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Most third-party tools are more to use for monitoring performance, query load time, profiling, no. of function calls, JS load time, HTML best practices and mobile usability. Below are the third party tools which I would like to prefer for auditing Drupal website.
New Relic provides deep insight for drupal website, includes Database performance, Modules Monitoring, Apdex, Function performance and front-end performance, it also provide the Real User Monitoring (RUM) which actual gather the time information and show you which hotspot in DOM rendering time may be causing your page to take several seconds to load.
XHProfiling measures the relative performance of your application at the code-level. it captures things like CPU usage, memory usage, time and number of calls per function, as well as capturing a call graph. The act of profiling impacts performance
Being a Open source of Drupal, there are many modules available which also help us in auditing Drupal site. These modules can either be independent or may use third party services. For example coder, xhprof, security_review, Dcq, Hacked, Security_review and Drupalgeddon