Faster hardware doesn't always translate to better graphics. The PS2 is the second-slowest system of its generation, just ahead of the Dreamcast, but it's capable of unique graphical effects that other systems and even the PC cannot easily replicate due to the PS2's unique ability to quickly process huge numbers of transparent textures; only recent PC hardware can replicate this through shaders; it was impossible at the time. That's why all ports of GTA San Andreas look dull and lack the complex effects of the PS2 original, even if they are better in some regards (like shadows). Mods can replicate this sometimes, but in case of San Andreas, this was only achieved in recent years - and I'm not aware of any other game having received the same treatment by modders.

This also applies to the Sands of Time trilogy. PS2 versions are better looking than other console versions and the PC ports. The best experience with it is through emulation. You get the high frame rates and resolution of the PC version, but the unique atmospheric effects that are only present on Sony's system. Higher-res textures alone can not make up for this, let alone the ones you linked to, which just deliver ugly AI upscaling noise instead of actual detail.