The PSP isn't due out for at least another 9 months, so it's not like we can verify when a developer makes lofty claims about the system–BUT…
Kazunori Yamanouchi, producer of the upcoming Gran Turismo 4, stated today in a Sony-sponsored interview that the PSP version of Gran Turismo 4 (Working Title: Gran Turismo 4 Mobile) will be a port of the PS2 version and approach the PS2 version in terms of quality and content.
In the interview, posted on Sony Japan's "PS World" Web Site, Yamanouchi states, "Expectations aren't as high for the PSP compared to the PS2, because development expenditures are so low, but its hardware performance is like the PS2."
Yamanouchi goes on to explain, rather abstractly, that some cutbacks may need to be made with respect to story or due to certain hardware limitations, but that the PSP game will have all of the content of the PS2 version and that the PSP version will be on par with the PS2 version in terms of graphics, audio, and overall quality of play.
Gran Turismo 4 is due out this winter for the PS2. Gran Turismo 4 for the PSP is in development.