It's amuzing people still have the "which one will win" mentality. Wasn't the PS2 supposed to obliterate the GC and the Xbox years ago? Didn't the PS2 win? Why are the otehr two out there yet?
It's almost certain the PSP is going to outsell the DS, since it got more idiot-baits built-in, unless Nitendo starts making out DS GTA clones out of the blue. But I doubt the DS will fall behind as much as the WonderSwan, Lynx and the Game Gear did.
The whole story about the two handhelds not competing entirely *is* true. Actually they only compete over a certain portion of the market, while both aim to catter different untapped markets. Follow my thinking:
The portable market is a whole different beast than the console maket. While the two audiences intersect at points, there's a bunch of console gamers that never really cared about handhelds, and handheld players that don't care much about home consoles, or seek a different experience in a handheld game than in a console game.
Let's call them the PlayStation market and the GameBoy market.
Sony's strategy is offer home-console "quality" experience on a handheld. The PSP is some sort of new generation Nomad, with deep pockets. It targets the PlayStation market. While it will surely have gameBoy-ish games (like Lumines), those game will be left out of focus in favor to countless "hardcore" games. That's a market untouched by handhelds up to now.
The DS moves in a whole different way. The "gameboy" market was always split into two major publics: gamers who also play consoles, and not-so-gamer people who don't play consoles at all, but like the simplier, quickier play experience that has been offered in handhelds for years. The PSP might eat a bunch of the first half, but the not-so-gamer people might be a bit scared off by it.
The DS is also trying to catter to an untapped market: people who don't play console nor handheld games at all. It's a much harder endeavour than the PSP's, that's for sure. It's hard to tell if the solid DS sales up to now came from this new market, or from the traditional handheld market.
It will never appeal to the "hardcore" gamer. But since the previous gameboys didn't do it either, there isn't really much of a market share lost to the PSP here. It's just that the PSP will appeal to an extra consumer market, and that will boost it's sales with sure.