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
SH3 and SH4 more than the others. SH1 looks great for a PS1 title, but it is still very much a PS1 title. SH2 looks decent but it has some rather awkward looking character models. SH3 looks fantastic throughout, and while SH4 also has incredible character models the actual levels you play on are pretty barren and not that great to look at
I was floored by the faces in SH3 and couldn't believe they were rendered in game at the time.