It will be INCREDIBLY hard for sony to "dominate over" nintendo in the handheld market (please don't think I'm a nintendo fanboy or anything, I own a PS2 after all) simply because nintendo literally owns the handheld market. Remember, back when only the orgingal gameboy was out, it was competing with the Lynx and Sega's Gamegear, both clearly technically better systems. However nintedo kept its crown simply because it knows how to do handhelds. I have read that Sony's PSP will have the ability to play movies, music and psp games. However, i have also read that it will have from 2.5-10 hours of battery life (10 for mp3 playback, 2.5-3 for intense gaming). If the battery only lasts for 2.5-3 hours, that is a serious problem. Also, the DS will be backwards compatible. I think that if developers can figure out how to make great games incorporating the two screens, touchscreen, WiFi, and bluetooth in DS, it will be easily be the better sy stem. At worst, you'll have a system with great new games from nintendo, and the entire GBA library (which everybody knows is great). Also, I think many developers trust more nintendo in the handheld market.

NOW, as to the N64 argument, the nintendo 64 graphics greatly surpassed those of the PsOne. Think about the great games that came out with the N64: Mario 64, Starfox, Smash Bros.,etc. The main problem with the N64 was that nintendo decided to use carts instead of CDs, which cost less and allow for better sound, and movies (this is why Square and many of the other RPG makers went to the Sony. I really can't see nintendo leaving the console scene anytime soon. In fact, I think their next console is really going to be sometehing special...

EDIT: oooh 69 posts hahaha