The games here are
Final Fantasy VII (1997) vs Final Fantasy VIII (1999)
Parasite Eve (1998) vs Parasite Eve 2 (1999)
Resident Evil 2 (1998) vs Resident Evil 3 (1999)
(You could place Parasite Eve between FFVII and FFVIII since it came out between the two and was used to prototype some of the tech for FFVIII)
The leap in quality with the human character models is especially impressive. Look at Sephiroth’s beautiful visage here and just think that Square went from that to feeling like their animation was convincing enough to carry an entire sci-fi drama movie with a realistic human cast in less than 5 years
spoiler
Then of course you had Oddworld Inhabitants who came right out the gate with movie quality CGI. Their characters all being fish-faced aliens instead of humans probably helped
I don’t think any of these were made with the PS1s engine. It’s a CD system so I assume they just made cutscenes on a computer and ported them as video files.
I think it was probably a case of these companies investing more and more money and/or hiring compent CGI studios after realising that these impressive cutscenes (for the time) were a major selling point for the system.