Probably the first thing to ever compel me to visit that rat infested dump
How involved is Capcom?
Nope not really. PSP rarely used it's full CPU speed to conserve on battery, and with Arm, processors you already take a hit on performance. PSP has none of the rendering hardware the PS2 has, the PSP had to do more in software than the PS2.
Also despite the PSP CPU is on par on the PS2's it's doing like 1/3 to 2/3 the total capability.
The PSP CPU does 1 - 333MHz at 32 bits but it usually runs at 111MHz. The PS2 runs at 300 MHz 128-bit integer SIMD, 128-bit floating-point SIMD and ran rendering in Hardware as it has dedicated rendering and video hardware. The PS2 might have the same clock speed but ti's doing 4 times the work of the PSP at each clock cycle.
The graphical abilities like two similar PCs (same CPU) but one running Intel on Board HD graphics and the other PC running a Nvidia 1070