There has been an ongoing explanation for a few years now regarding which of these handhelds is better. The PSP features a larger screen which is able to play movies, games, music, and browse the internet. The Nintendo DS features two smaller size screens, but with touchscreen capabilities which almost all games released for the DS take advantage of. So the battle of the handhelds begins! For the sake of this argument, I'll be referring to the PSP Slim and the DS Lite as they are the newest versions of each handheld.
The PSP Slim 3000 is the newest model of PSP. It features the same slim design as the PSP 2000, but it adds an anti-glare screen which makes playing in the sunlight a bit more easier. Also included with the PSP 3000 model is a built in microphone which allows you to essentially use the PSP as a phone with the Skype software that comes installed on it. The 3000 also features the same capabilities as the two older model PSPs, with the ability to play movies, games, music, and browse the internet with access to WiFi.
The DS Lite, which is a slim version of the original DS, features the touchscreen with stylus, along with the ability to access the internet through WiFi. The ultimate decision of what is better here comes down to the style of gameplay you enjoy, and how much accessibility you want while out and about. The games available for the DS are focused more towards a younger generation of gamer, with games featuring Sonic, Mario, and Pokemon predominant on its greatest sales list. These light hearted games are great for some fun, but most of them offer little replay value, outside of the Mario franchise.
The PSP on the other hand, appeals to the older generation of gamers. It features such dark titles as Manhunt 2, God of War, and Socom. However, the PSP is not without its share if light-hearted titles. Games like Patapon and LocoRoco have provided PSP gamers with hours of fun with their new and innovative gameplay.
The PSP should be the choice for gamers who enjoy more mature games with a bit less interaction, as well as a movie player, music player, and web browser wrapped all into one handheld system. While the DS does not feature many of these extra aspects, it does one thing well, and that's good light hearted gaming.