While the PSP screen size and general layout of the buttons stayed the same during the x000 iteration, there are noticeable differences between the models:
PSP-1000 vs PSP-2000
- Speaker holes moved from lower side to upper side
- Button placemenet changed
- Different UMD slot, UMD switch on 1000
- Headphones port moved, different power connector
- IR port on 1000
- 1000 is thicker
There's a radical physical diffenece between the 1000 and the later models, therefore a cover intended for the PSP-1000 would probably not fit the later models and vice-versa.
PSP-2000 vs PSP-3000
Other than that (and different internals), PSP-2000 and 3000 are pretty much the same, I would assume a cover made for either will fit the other model, but it'll require some modifications on the bottom part, to fit the different button shapes and microphone hole, and will look different on the back cover because of the different ring thicknesses.