Japanese graphics house DMP has confirmed that their PICA200 GPU powers the Nintendo 3DS. Eurogamer's Digital Foundry goes in-depth on the hardware and points-out that the PICA200 is a fairly old design that was completed more than 5 years ago. This puts the horsepower of the chip below the PowerVR SGX535 that powers the iPhone 3GS and iPad. Digital Foundry also clarifies that the chip does not support the OpenGL ES 2.0 standard that Apple's recent devices have utilized.
According to DMP, the PICA200 is capable of rendering 15.3 million polygons per second, with a throughput of 800 million pixels per second. For comparison's sake, the iPhone 3GS's GPU is able to render 28 million polygons per second with a throughput of 500 million pixels per second. These numbers may be somewhat deceiving though as Apple does not allow low level coding to hardware as is typically done when programming for consoles and portable gaming devices.
Futuremark put together a demo highlighting the PICA200's graphical capabilities at the time of its launch. It should be noted that this sort of graphics demo does not account for the processing power needed to run game logic and AI routines.