What we have here are screenshots from TimeSplitters 2. On the left is the GameCube version running on Dolphin and on the right is the PS2 version running on PCSX2, both upscaled to 1080p.
You might notice the lighting being slightly different, but if you look closer, you can also notice something funky going on with the graphics on the upscaled PS2 screenshot:
When you use the hardware renderer to upscale TimeSplitters 2 in PCSX2, you get headache-inducing ghosting that's persistent throughout the entire game. Note that this is with PCSX2's default game-specific hardware renderer fixes enabled, and to be fair, it looks even worse without them on. You can get rid of the ghosting if you enable manual hardware renderer fixes and set SkipDraw to 1. This gets rid of the ghosting but it also gets rid of other effects, like the radar screen:
I assume there's some kind of depth of field effect that gets broken when upscaled. Unfortunately, plenty of PS2 games have similar ghosting issues. Depending on the game, you can use SkipDraw or enable cheats that disable whatever specific filter or effect is causing problems, but it's usually at the cost of breaking something elsewhere
Why did the PS2's Graphics Synthesizer have to be so weird 
Texture on that tunnel wall looks better on the gamecube version but the computer model looks better on the PS2 one.
I forgot to mention the textures. Yes, the GC definitely comes out on top with that here too. It's interesting- the GameCube minidiscs hold almost three times less data than DVDs but on the other hand the PS2 had a tiny amount of VRAM so I guess it evens out