PS2 largely pulled away IMO because Microsoft stupidly decided to get involved in the game industry. That basically cut the competition in half, so instead of having one central competitor, it was divided into two.
IMO, MS should've pushed harder for a deal with Nintendo and thrown their support behind the GameCube, then you would've had a more competitive hardware generation. And yes Nintendo should have been less stubborn and realized that allowed some Windows CE to run on the back end was a small price to pay to not have another massive company to compete against.
That was more of a factor than DVD.







