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
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.
XHProf
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
YSlow
YSlow analyzes the webpage and suggest ways to improve page performance based on rules (Minimize HTTP Requests, Use a Content Delivery Network, Cache-Control Header, Gzip Components, Put Stylesheets at the Top, Put Scripts at the Bottom, Avoid CSS Expressions, Make JavaScript and CSS External, Minify JavaScript and CSS, Avoid Redirects and Remove Duplicate Scripts etc). It also supports Smush.it and JSLint. YSlow can be configured in the system directly and is available for Firefox, Chrome, Mobile/Bookmarklet, Opera, Safari, Command Line (HAR), PhantomJS, Node.js Server, Source Code. Other Third party websites which monitor your site based on specified URLs and report what part of the sites can be improved. These can be JS, third party URLs, services URLs, HTML markup for desktop users and mobile usability.
Contrib Modules
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
