Bit of pedantry first.. all of this stuff is on the same chip, OMAP3530/DM3730. NEON in particular is part of the CPU, it's not a separate thing.
SGX is the GPU (graphics core), and rendering graphics is really all it's good for. On newer GPUs you may be able to offload other sorts of work to them but that's not really an option here. On Pandora using the SGX can mean a lot of overhead spent in drivers. Getting the best performance out of it is challenging, and for emulators the features exposed by the API (OpenGL ES) may not be a very good fit for what the console does, and may need too much overhead to make fit. So a lot of emulators don't use it, even if they have 3D. The only one I know of that uses it is mupen64plus. A PS1 emulator could probably use it but it wouldn't be as accurate as the renderer we have; if you look at PC PS1 emulators they have a long history of severe graphics problems and lots of hacks to try to work around them, because of using PC graphics cards. It doesn't really help that OpenGL ES 2 is often a more restrictive API than ones the PC plugins used. For 2D console emulators trying to use the SGX just isn't worth it.
DS emulation in particular is a worse case, since it has both a 2D and 3D engine and has to combine the output from both. The 2D part doesn't work well for a GPU, and if you do the 2D in software and the 3D on the GPU then you have to read back the contents of the 3D render buffer which is really slow. Some PC emulators do have GPU-based 3D emulation but they tend to offer software emulation too and it's typically faster, sometimes much faster (and much more accurate).
NEON is a set of instructions for the CPU, that let you perform multiple operations in parallel (Single Instruction Multiple Data, lookup SIMD on wikipedia). Not a lot of emulators are using it but the ones that are use it to emulate high level things like graphics and audio, or parts of the console that were already vector processing like geometry transformation.