These kinds of comparisons are difficult to gauge properly in such a video due to all of the variables involved. Depending on what games are chosen to be compared or, as someone else mentioned, if emulators are used, it can skew the results. The true comparison is to view the results in person and while the PS4, as of right now, isn't comparable by this metric, the biggest leap IMHO is easily between the PS1 and PS2.
The PS1 was incredibly rough around the edges regarding 3D graphics and really didn't age very well. Comparing launch window PS1 games like GameDay, Madden or Battle Arena Toshinden to launch-Madden or TTT on PS2 is a mammoth leap – not just via screenshots, but especially in motion.
PS2 fixed a lot of the big problems and flaws (very blocky poly models, pixilation, etc) that were unavoidably present on PS1, whereas the PS3 mostly made improvements. It's not that the technical leap isn't there – it is – but the perceptive leap isn't as large to me. The gap between PS2 and PS3, while certainly noticeable, is not as profound, and I certainly don't expect as big of a perceptive leap between PS3 and PS4 either.