There's a simple answer to this - YES!
The PSP first introduced a while back now, and it's still as popular as ever. It's the most expensive hand-held console on the market right now - and too right it should be.
I've got both a PSP and a DS Lite. Both are fun and the DS is fresh but Sony stick to what they do best - great graphics, hot games and huge number of game enabling wireless mode.
Okay, so the PSP has only one screen, and it's not touch. Who cares?
The DS does not make use of the screens, with shallow games like Mario 64 DS showing nothing but a map on the touch screen.
PSP's 4.3 inch screen is bright, big enough and quality. Grand Theft Auto Vice City is entertaining and definately makes use of the whole screen to the fullest extent possible. It's like a smaller PS2, even the graphics compete with it, and wireless gameplay make it even better when you can play with friends!

The PSP's battery is amazing. With the screen on the brightest it can go and the sound up loud I can play games for hours without needing to charge. The indicator is also handy when it flashes you plug it in - simple. Although it's not place very well as your thumb obstructs it - no worries though. When the battery gets very low the PSP will automatically go into sleep mode and save your current place in game - Handy.

Another thing that strikes me about the PSP is the huge choice of games available for it.
There's shooters, RPG's, Racing games, Logic games like Mercury Mayhem and Loco Roco, there's an enormous choice, no matter your taste you WILL find a game that you'll enjoy playing on the PSP.

Playability is great. The thumbstick is good for navigation when racing or shooting, the arrows are good for games like Mercury Mayhem and the L and R buttons mean more actions are at your disposal - similar to the controller of a PS2. I'm already bored of my DS Lite and they haven't been out long.
I still enjoy playing my PSP.

Nifty function of the PSP don't stop there. You can even use your PSP as a DVD remote for your PS3, or as a controller in some games - which turns the screen of the PSP into a map or rear view camera in racing games, much similar to the DS's Two screens.

If you're a serious gamer or want hours of playability from your handheld console get the PSP.
If you're looking for something original, but shallow, maybe if your shopping for a child or someone you know is going to get bored regardless - get the Nintendo DS , it's much cheaper and i'm sure a child would love it.

Hope this guide has been helpful.
*Vandy*