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
It started out way back on the SNES. They were doing joint development with Sony on a CD expansion peripheral (hence that weird port on the bottom of the SNES console) but the project got scrapped. Oddly enough, around the time that Commodore went bankrupt once and for all, Nintendo's name was floated as a possible buyer so they could take over manufacture and sale of the Amiga CD32 system, which was basically just an A1200 crammed into a game console. That just turned out to be a rumor floating amongst Amiga nerds, though, when German business genius tech giant Escom bought out the rights to the Amiga and made the CD32 into the game industry titan that still dominates the global market today.
It's amazing how much business bullshit completely changes the course of a thing while taking none of the public eye