I don't know of any quality issues but for me, my PS2 games look better on my PS3 but only marginally. PSone games look a lot better. I think it really comes down to the type of display you use and the cables in which you connect though.
I play on a 40" 1080p Samsung. My PS2, connected with component cables looks like a pixelated mess. Connected with S-Video cables, it looks, OK. PS3 in this case, makes my PS2 games look smoother and at a slightly higher resolution.
Using the S-Video cables, PSone games look ok on the PS2 but also shows many flaws.(as do the component cables) Using FF VII as an example, PS3 smooths out the image the way it would normally look on an SDTV, while slightly (appearing to be) up the resolution a little.
I hope that helps. :)
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