The orig PSP headphones are terrible tbh. The quality isnt up to much and although for health and safety reasons they have been volume limited, it can be quite annoying.
As a DJ, I can recommend a whole rande of hi tech headphones, but for your needs, as mine when it comes to the PSP - I find these excellent value for money:
Sony - in ear headphones
A good choice although not to everyones liking, they can prove to be slightly uncomfortable. They plus side is that all outside noise is totally erradicated. All you hear is the device you are listening to.
An alternative to this would be:
these. These folding style ones have very good sound response.
These are merely 2 suggestions as the range is phemomenal these days. As Sue commented, any headphones will wrok fine in the DS and the PSP, but I prefer a bit more clarity and quality in my ears.
Any more advise dont hesitate to ask.
Hope this helps you.