I have to disagree with most posters that say PSP software is crap compared to DSi. I would say MOST DS software is shovelware. Biggest selling games for DS are the ones aimed at little girls (imagine brand, cooking mama etc.) , children (nintendogs, petz, etc.) or older people (brain games).
For core gamers DS library is not very extensive. It is mostly nintendo FIRST party software and, lets face it, Nintendo brings out 1 game for each franchise every few years. There are some really good games but like PSP library a lot of them are PORTS.
As far as innovative controls are concerned not a whole lot of games are purely stylus based and some are easier to play with normal controls (IF it is supported).
My PSP gets a lot more time than my DS. I like the PSP mechanism of puting the console in sleep mode. I also like the fact that I can use PSP FAT's batetry with it to increase battery life.
I like the DS mostly for its ability to plays my GBA games as well. DSi can NOT do that.