Yep, the issue is there in hardware native mode. This is what it looks like in hardware mode, native res:
If you look closely, you will notice that all sorts of post processing layers are off-alignment.
The bloom layer is done right (at this res, at least), but it's literally just a hack (on the developer's side) that takes whatever bright parts are in the scene that need to be given bloom, downscales the image and stretches it again, brightens it up, then moves it to a slight offset to simulate a bloom-like effect. It's probably impossible to make this look accurate at high resolutions, unless you hacked the game's code to downscale it by a greater factor depending on the resolution the image is being rendered at. The next best thing is to keep the pixel offset constant throughout every resolution so that you don't notice these problems too much (i.e. the bloom gets weaker when you raise your res higher).
The lighting layer and shadow mask, however, are off-alignment. It's hard to see in the screenshot, but Dante's coat has a weird faint double to the right of it. To the right of Dante's head is a weird shadow. These things are artifacts of a completely misaligned post processing effect that deals with some of the lighting and shadows in the game. (Most PC games just have baked textures and lighting effects where necessary and don't need a post processing filter to do this, but the PS2 has limited memory and needs hacks like this to avoid having to keep a huge baked image with the lighting, instead using post processing to save memory (so they can just use tiled textures and include a rudimentary low-memory thing to store the lighting information for the PP to interpret) and add some extra flair to the image at the same time.) Notice that in the below software render, the artifacts I mentioned are not there because the alignment is perfect. In the above hardware render, the alignment shows where Dante's head overlaps the lightmap, casting a mask over it to negate the lightmap according to Dante's head shape and profile, so that the lightmap behind it doesn't render on top of Dante's body. However, it's not in the right place so it just looks like some kind of retarded shadow. The effect is similar for Dante's cloak, which casts a faint glow to the right (same distance as the shadow from Dante's head) because the cloak overlaps the lighting map, but also needs to be brightened by some other parameters, causing the end result to be slightly brighter than the background rather than darker.
On software mode, it looks perfect: looks and plays exactly like on a PS2. But it offers no real benefit over using an actual PS2 unless you really want to use mouse/keyboard or an XBox controller, or perhaps record some videos. FYI to whoever googles this thread in the future, you can get used PS2s for like $50, and can get PS2 games for very cheap if you know where to look, so money and availability should not be an issue for anyone.
Software mode: