It is something we improve with every release actually.
Its a very difficult process to be honest to compare multiple sites with multiple test metrics, but its something I will try to tackle.
The first test you posted, when clicking on the link, this is what I see (I am screenshoting because they vary over time).
thirty bees, http://storage6.static.itmages.com/i/18/0123/h15166741159059172af10a6ed5d.png
PrestaShop 1.7 http://storage8.static.itmages.com/i/18/0123/h151667417027097160682054075.png
I would be lying if I said we beat them, because we clearly arent. But why aren't we? That is the better question to ask. In a round about way, it is because we care about data security, we care about SEO. To be point blank, it is because we use an SSL certificate and secure the site. Notice that PrestaShop's demo is non https. Also look in the screen shots I posted and the links you posted. SSL negotiation is taking around 500ms. If we wanted to put out a demo that was pure speed without best practices, we could.
Here is what our demo does with SSL turned off. http://storage2.static.itmages.com/i/18/0123/h15166744117583843_ddcee009c6.png
We beat them in that case.
TTFB is a meaningless metric in my opinion. Like I wrote about in a post last week, what is better a .2 second ttfb and a total page load of 4 seconds? Or a .5ttfb and a full page load of 2 seconds? Are users going to notice the 2. seconds or the 2 seconds? I err on the side of the 2 seconds.
I prefer the raw speed approach. If you look at this test
https://tools.pingdom.com/#!/dTflqp/http://fo.demo.prestashop.com/en/
https://tools.pingdom.com/#!/d31zoF/http://front.thirtybees.com/
Which loading time would you prefer? Then scroll down and look at the ttfb. We lose that. Which is more preferable though, a site that loads in .6 seconds or 2 seconds?
In the future its going to get even more complicated that this. Lighthouse is replacing PageSpeed as the preferred metric, its metrics are more meaningful than PageSpeed, it is more of a real world metric. It takes into account not only the loading time of a site, but the processing time as well. I am sure you are like me, you have loaded a site on your phone, it comes up with a blank screen and the bar is spinning. Does that mean the site is still download? It does not actually, your smaller phone processor could actually just be parsing everything that was download.
This is where Lighthouse comes in. It does not just grade on TTFB or complete download of files. It rates off how quick a user can see the first paint of your site and how quickly a user can start using your site. These are more real world and meaningful.
From my tests just now.
http://storage3.static.itmages.com/i/18/0123/h15166758288703700ddcee009c6.png
http://storage4.static.itmages.com/i/18/0123/h151667588366811283dfd302eaf.png
This is something else we win hands down in. In the future it will only get better after we move away from the 1.6 themeing style and more to our own.