Impossible to say. The PS2 was in a prime situation and the landscape was different then. Also, it's been demonstrated that many people who fell victim to the RRoD were content to stay with the 360, perhaps because they liked it until it died, or because they already had a personal library assembled.
I doubt the PS3 would have "won" North America regardless, give what hits Halo and Gears were with the shooter crowd.
People keep comparing the PS3 to the PS2 despite circumstances being a lot different. The same thing is likely to happen with the Wii U, even though the way the Wii went viral with the casual crowd was a lightening-in-a-bottle situation that can't be expected to happen in consecutive generations. I'm already rolling my eyes at all the soon-to-be "the Wii U is a failure because the Wii sold better" posts.
Besides, Microsoft spent large sums of money at the start of this generation buying times exclusives. They weren't going to be denied a share of the market.
