Well, youtube videos come from all kinds of different sources: A VCR taping from the TV output, a VCR taping a TV, a video capturing board, ripped directly from the disk....

When the video is ripped directly from the disk, it runs much better than on your PS2. As an example, the FFX2 sphere scenes with Shuyin / Lenne were choppy and bluish on my PS2 but the digital video on the game disk is very clear and lifelike.