For me, the PS2 is the definitive way to play PS1 games. It has a bilinear texture filter that's optional (You have to eneble it at every power-on, which I find annoying...). But it essentially smooths out the textures from pixelated messes to smoother looking messes, like the N64 does. You still get the weird texture shimmering from the lack of a floating point, but most games look much better with this setting enabled.
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I know this example is PS1 vs PC, but it still looks roughly like what the PS2 does to the game's textures with this enabled. It's the only way I like to play PS1 games, for an authentic experience. (And I wish the PSP could tap into the texture filter when playing PS1 games, just like the PS2 had. Sadly, there's just no equal.)
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