Its hard to compaire a 3D world, vs a lock perspective + 2D background.
But in terms of character models (which both have) FF9 blows Perfect dark waaay outta the water. Like thats not even close.
So geometric detail, model vs models isnt close.
Shadows are the same, just a blurry blob underneat the character models feet, in both games.
Lighting? maybe it goes to Perfect dark, but again its hard to compaire when the 2D backgrounds kinda get in the way of that sort of compairsion.
Textures are better in FF9 too, theres much higher detail there.
The battle sequences in Final Fantasy 9 were fully 3D, not using a 2D background, hence why I used them in the comparison. (You must not have watched the video.)
Geometric detail of Perfect Dark was certainly a step up overall, there were far more polygons on screen at any one time.
Shadows weren't the same, Perfect Dark had some dynamic lighting thanks to it's TnL engine and baked shadowing.
Carrington Instute level actually showcases this really well with shadowing on various surfaces, even some reflectivity, the PS1 just doesn't hold a candle to these effects. - These are "clean" images, but it showcases the detailing of what I am trying to point out... But hey, if you can point out a PS1 game with texturing that is on Par, with shadowing detail, lighting details, transparencies, reflections and so on all in one scene... By all means, please showcase it.
And like I said. Perfect Dark wasn't even the best N64 game visually, but it was certainly a step up over Final Fantasy 9, especially with the effects she was pushing.