Size
A PSP 1000 is 3 ounces heavier than the 2000 model and slightly larger all around, hence their Fat and Slim nicknames.
Screen
While screen size and color depth are the same on the two models, the PSP 2000 has backlighting capabilities.
Speed
Both models have the same CPU, but the PSP 2000 model has twice the available memory, so it run noticeably faster than the PSP 1000.
Battery Life
Battery life is essentially the same in both. With a standard battery, they offer three to six hours of game time, depending on factors such as screen brightness and wireless connectivity. However, only the PSP 2000 is compatible with Sony's PSP Extended Battery Life Kit.
Peripherals
PSP 1000 models are incompatible with newer PSP headphone sets. They also have no video-out port, so unlike the PSP 2000, they cannot be hooked up to a television. They also lack a built-in microphone and thus Skype capabilities via the PSP's built-in WiFi.