Your testing methodology is abit off.
If you notice the test you did of TB on Byte Check there is a redirect in the test you did, always make sure you test with the right URL since a redirect can add extra time to most tests, but for me the TTFB of http://front.thirtybees.com/ is about 200-400ms
The way you testet PS is off by a lot, when you test there site you have to remember they use a landing page, where the demo store is loaded in a iframe, this is not countet in to the TTFB, if you go in to the source code and find the iframe, and get the link from there, the results are very different, with the iframe approach the result is 200-300ms – but without the iframe and direct link it hits 400-500ms, so it’s about 200ms slower then TB.
And pagespeed insight is just flaky as hell, a lot of things can be at play here, server location is normally the issue when it says reduce the server reply time, since PageSpeed Insight runs off servers in USA, and I am not sure if PS might use some sort of gateway that sends you to a version of their test site closer to USA when you test with insight.
And again testing sites against each other with different world locations is unfair in general, since some sites will have better scores ex in EU, some will have better in US and so on, the latency has to be taken in to account.
The most important metric is how long it takes before your user can see content and start using the site.
And again theste demo sites never use modules, or have a ton of products, so they will show very different metric compared to a more real world example, the reason i dont mention magento, is that the cost of getting a fully working magento site for production is about 6-8 times higer then Prestashop.