Its hard to give a valued answer without showing bias. I've spent substantial time with both systems and in my experience, I found the DS to be more to my liking. For value, PSP is the obvious choice if you want to turn it into a portable ROM. The DS has a larger library, and I'm surprised no one has mentioned the fact that its backwards compatible with GBA games, giving it an even larger library. It comes down to why you want both. Crisis Core or World Ends With You? FFT:War of the Lions or FFIII DS? Dracula X or Phoenix Wright...

For me, I don't care for ROMs cause they are counterproductive for the industry. If you live in a country that gets shafted alot (not US or Japan) then I can completely understand the allure of Homebrew. Beyond that, I wasn't too impressed with either Crisis Core (seems I'm one of the few on the forums who hates it) and Valkyrie Profile. I have issues with the PSP cause the vast majority of its games that are appealing to me are ports of already good games. It suffers from the same problem I had with the GBA. Lack of good original content.

Though I must say, tech-wise I'm far more impressed with the PSP. I really enjoyed the ability to shut off the system and it pauses exactly where I left off. Its definetly more user-friendly as a hand held.