Question : Determine website load speed and see how it compares against other websites

Simply request: I would like to determine my website's load time and see how this compares against other websites. I do not wish to type the other websites myself in a browser - I wish to see automatically how my website stacks up against previous tests or just general accumulated stats.

Answer : Determine website load speed and see how it compares against other websites

I am not sure if this is what you search for, but GMetrix uses both YSlow and PageSpeed in order to compare websites:
http://gtmetrix.com/