If you want to compare two website’s loading time, you should check out whichloadsfaster.com. The service allows you to see which website loads faster and by what factor. It suggests some random matchups when you first visit the page like Google v. Bing, Apple v. Adobe, Amazon v. Shopzilla, and TMZ v OMG! but it’s more useful for running your own tests on websites you are interested in.
Just running a simple comparison is easy enough, you enter both URLs and then run the test. You can configure settings so that the tests run simultaneously or sequentially, in case testing the two pages would unfairly and unpredictably affect each other. You can compare any two websites or the same site. You might see how much faster/slower an article page is versus a home page.
If you’re testing new hosting, you might be able to access the same site via a dedicated IP address on one server and via domain name on the other to test out the new hosting. You could also be testing the increased responsiveness of a new service. If you had litespeed, varnish, or nginx responding on a select port and apache responding on another, you could run the test to see how things compare on the same server.
All of it just provides more information about a server, whether it’s yours or a belongs to a big company. The information can be helpful to compare.
Check out whichloadsfaster.com.
If you’re looking for other tools, check out webpagetest.org and my favorite Tools.pingdom.com.