Playstation is going to remain the dominant system, not necessarily because it will be the best system, but because of the way their competition conducts their businesses.
Playstation's game plan, both for their original and for PS2, was essentially to get as many distributors as possible to format for their product. It meant the PS and PS2 had a lot of crappy games on the market, but it also made way for some very good titles that would have otherwise gone unnoticed.
Nintento's game plan, all the way back to the days of 8bit Nintendo, has been to recycle the old mascots over and over again (Mario Bros., Super Mario Bros., Mario 64, Mario Sunshine). With both N64 and GameCube, this left their gamers with only a handful of games to choose from, so most people that first chose the Nintendo system ended up getting the Sony system at a later time.
Microsoft's plan seems to be, for the most part, to see which games Sony's clientelle enjoy the most, then offer only those titles and a few others for their platforms (in fact, Microsoft's original game plan was supposedly to format X-Box to play PS2 games, and to format the X-Box games to not work in a PS2). This allows Microsoft to boast having the better quality games, but since the same titles are available for a system with a wider selection, most consumers can live without trying the three or four games that are available for X-Box, but not the PS2. Also, most people around the gaming age have heard about how Microsoft conducts 'business' in regards to programs like Netscape Navigator and Corel WordPerfect, so a lot of their potential consumers don't want anything to do with the X-Box.
The best quantity and quality will always be for the PC, but gamers will purchase fewer titles because they will take up memory on their computer, and will be more hesitant to install a PC game since few PCs come in too many different variations for every game to always work properly. The most popular PC games will be games like the Sims and Neverwinter Nights, which are formatted in such a way that user-created hacks can be easilly implemented. Beyond those and the occassional Sim games, however, most people will just wait for the hot PC games to be available on the consels (it worked for Half-Life, Sims and Baldur's Gate, didn't it?)