Fighting games (JUS and Bleach are the only great fighter in the DS imo) and Shooters definitely belong to the PSP. DS has alot of those great quirky games (Warioware, Ace Attorney, Trauma Center, Prof. Layton) JRPGs belong to the DS although PSP still has some great upcoming RPGs. For upcoming games, I definitely like the PSP's lineups better (KH, SO2, LBP, Dissidia, Agito, PE3, Patapon 2, Resistance, etc)
The DS has games that are...different. Yeah uniquely different. Although PSP has some weird games like Patapon... Well as always it all comes down to preferences.
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