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Pros
Pro The results of speed tests are incredibly detailed
You can dig deep into your results down to the root to find out what are the issues that are leading to your website being slow. There are a lot of options which you can select to narrow down your results namely timelines, content breakdowns, processing breakdowns and incredibly detailed performance reviews.
Pro Ability to select browsers for testing
If you'd like to go a step ahead of just speed profiling your site and see how not only how it performs but also how it appears on different browsers, Webpagetest would be the best option for you. Due to its vast range of browsers available (From IE7 to Chrome on Android or even Safari on iOS)
Pro Test your website from different locations
If your website serves visitors only from your own city or country. It'll be a good idea to speed test it using one of Webpagetest's servers in or near to your area.
Pro Speed Index Measurement
Provides an excellent user perception metric, Speed Index, of how much content above the scroll is completed quickly.
Pro Filmstrip
Can be set to provide a film strip of the page loading
Pro Free
Pro Can handle sites behind Basic Authentication
Often sites in development are protected behind basic auth