DSi. I love the PSP and its excellent for on the go media but i must admit that the DSi is a better games console.
What about an iPod Touch? Costs about £150 and has many thousands of games/apps that can be downloaded for free or for 59p-£2ish. My kids (6&9) want and use my iPhone(same software as ipod Touch) much more than their DS's where games are upto £30 each. I could load up an ipod touch for a tenner and it would be far better fun than a DS with £100 of games.IMO etc...
DS all the way.
Nintendo consistently churn out games you can play over and over for years, the touchscreen is easy for kids and there's a load of really good casual stuff for grown ups to play too. I've not tried a DSi but our DS has survived a lot of dribble, dropping and general toddler based abuse over the last 2 1/2 years so they're pretty damn robust as well.
I just wouldn't buy a PSP, If I wanted that sort of console I'd buy a PS3 and live without portability.