I own both a PSP and a DS Lite and I would have to say without homebrew/hacking the PSP wouldn't be anywhere near how good it is. The DS has some really fun and innovative games. The PSP has a couple games that are almost 100% like the PS2 counterpart and more functionality.
Here's what makes the PSP bad:
loading on UMD (I ditched UMDs a while ago)
expensive
worthless firmware updates
low battery life
Here's what makes the DS bad:
cartridges hold not a lot of information
needs Supercard or M3 to run roms/homebrew
graphics are nowhere near as good as PSP
Both handhelds are very different and can't substitute the other one. Without homebrew/hacking I think both my DS and PSP would be collecting dust.
Final judgement: best for homebrew/hacking PSP
best for commercial games DS
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