The PSP is actually in many ways superior to the PS2. It has more than twice the internal memory for instance, which means it should be able to handle far better textures and sound samples, for example.
The 24bit color graphics will in fact look sharper because the 480x272 (or something like that) pixels are spread over a relatively small surface compared to the big TVs and monitors on which we see the 640x480 pixels of the PS2.
If it has the same power as the PS2, that means it can in fact do faster work on such a small display, because the amount of data needed to fill the screen is smaller. All in all, the biggest and perhaps even only drawback of the PSP against the PS2 will be ... yes, the smaller screen. Everything looks smaller. But even with the expected magnifying glass options you'll no doubt get for it, the graphics will look extremely good.
PSP graphics anywhere near as good as the PS2s graphics? Yes, who would have expected less?
I think you've been brainwashed by a very lazy and comfortable company who's held a monopoly so long it thought it could get away indefinitely with selling technology that will soon be 2 decades behind the times.