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 
My approach for years is just to use the GameCube version unless its a ps2 exclusive. Like even the deinterlacer can cause some weird artifacts if the game doesn't support progressive scan and pressure sensitive buttons still fuck me off. Also some games the opengl renderer just doesn't work properly I tend to run in software mode a lot of the time and have done for years. For example armored core 2 actually performs worse in hardware rendered mode lol. I use the built in lottes filter it makes the native ps2 res look nicer on bigger screens but i mostly ps2 on my steam deck where native res actually looks great. I also really just hate the high res look on classic games and it makes me shudder when I see what people do to ps1 games, i prefer integer upscaling.
But yeah I've had issues with ps2 emu for like a decade I'm glad it finally got a usable UI though
That's more of a 2D thing though, right? Anyway, all the edges in my PS1 games look sharp enough to cut paper
Personal preference but I don't like overly sharp 4k ps1 graphics. I prefer native res integer upscaled with CRT filters to try and replicate the original look as closely as possible. The dithering and warbling stays on in bed