I own a PSP and my 3 kids aged 7 -12 all have a DS.The trouble with the PSP is that there are very few great games available.The DS despite having inferior graphics and sound has loads of really good original games on offer many of which would appeal to an 8 year old.
So i would go for the DS.
the thing in the PSP's favour is that you can watch films on it and store things like music and photos so it has more functionality. I agree with bix about the range of games though but I am speaking from a girls point of view who doesn't play racing or football games (saying that I am addicted to the Everybody's Golf game) although they are constantly bringing new games out.
DS...hands down. It's aimed at younger kids anyway, and the interactivity and gameplay blows the PSP out of the water. The PSP is undoubtedly a more powerful, multi-use machine, but in terms of pure fun the DS is streets ahead. I own both, and i'd give an 8 year old the DS any day.