The PSP minis are not comparable to the iPhone apps in the sense that they restrict you from using any peripherals, download content or any network activity for a start. Not being a iPhone developer all I can tell you is that developing for the PSP should be somehow easy once you already checked out the free PSP SDK (ps2dev.org).
The free SDK contains lots of samples showing you how to use the controls, IO, and graphic capabilities. One major difference is that PSP doesn't support OpenGL, instead it has its own GL like API called GU.
GU programming is close to OpenGL without texture management support (this is an extremely basic comparison). For audio and video there is dedicated hardware that can decode mpeg4 and to speed up your code you have an extra vector floating point unit processor that is very fast and can boost your 3D and physics code.
There are however ports of popular game development libraries such as SDL, Allegro, ODE, BulletPhysics, etc.. that you can use as a base for your game development. So lets say that you master already SDL coding for the PSP can be almost trivial just by adjusting the screen mode and input of your game.
