Usually, they will give you input about what's good and what isn't. You should be aiming at a score of roughly 80% or higher, and a load time of less than 2 seconds. All of these tools have their own particular issues they look at, and they don't give the same website the exact same ratings, but the trend is usually the same. Let me discuss some of the above-mentioned services:
I often use the GT-Metrix service, as it measures both Pagespeed and Y-slow in one session, giving you a nice overview of both:
GT-Metrix provides a lot of details of why a site runs slow, or general advice about this, split up in separate items. As you can see here, the Pagespeed and the Y-Slow scores are slightly different, though both A-scores. In this case, I know Y-Slow favors Content Delivery Networks more and gives you a lower score if you don't have one. That is only one of the examples why the score often differs slightly. One nice thing about GT-Metrix is that if it finds non-optimized images, it provides optimized versions if you click on the item. GT-Metrix also allows you to monitor one site over time if you register, reviewing it once a day.
Pingdom gives you pretty much the same information as GT-Metrix. Usually, it detects the site to load faster then the GT-Metrix site, which is why you should not trust this value too much. Instead, focus on the individual items found. The waterfall tab shows you how the individual resources of the site load, while the Performance grade tab shows you the items which cost you most.
Very nice with Pingdom is that if you register, you can monitor one site for free (forever, including uptime), with 5-minute intervals. This is very nice for monitoring changes you performed on the site or server upgrades:
Google specifically encourages optimization of Above-the-fold content and visible content, which usually requires complicated tricks that are hard to achieve, like specifying CSS that only favors the above-the-fold content, where the rest of the CSS should only be loaded later. Therefore, it is very hard to get a score over 95 here, but that should not worry you too much, hardly any site does. JCH-Optimize has an Optimize CSS Delivery feature that aims to achieve this, you might give this a try, but make sure to check your site remains functioning correctly then.
A nice newcomer is DareBoost. It measures the main aspects of speed and performance, but it also throws in a few security and SEO checks. It is available in a free and some paid packages, but the free checks are already quite nice:
A tool with a different approach is Loadimpact.com. It does not just look at a single session, but it fires a load of dummy traffic with Virtual Units to your site and measures how your site can deal with that. Especially if your site is popular with many visitors, this might be a very useful thing to test. Loadimpact is a paid tool, but it allows you to run 5 tests of 5 minutes for free every month:
Fortunately, for most issues there is a solution, either within the Joomla core (like caching or Gzip) or using an extension. So in the examples above, most issues have been solved, and while for other issues, there is still room for some improvement. Note that these tools only give general advice, you should also use your own common sense. As an example: If your site loads a dozen full-screen images, the tool might tell you that the actual individual images are fully optimized, but it will not tell you that you're quite foolish, loading these super large images.... As a consequence, you could have really high scores with a slow site.... My own site is a bit of an example: My GT-Metrix scores are 99 and 99, but I had to use local @fontface fonts to achieve that. A single call to Google fonts could possibly be quicker, but I have no control over the caching-lifetime, since the font is on the Google servers, lowering my scores.
Also, while some tools have different priorities, a combination of tools plus your own common sense usually works best.
Joomlaseo.com is fully built and written by Simon Kloostra, Joomla SEO Specialist and Webdesigner from the Netherlands. I have also published the Joomla 3 SEO & Performance SEO book. Next to that I also sometimes blog for companies like OStraining, TemplateMonster, SEMrush and others. On the monthly Joomla Community Magazine I have also published a few articles.