What Darc Requiem said, basically. The first Xbox was just there to prevent a complete Sony monopoly - and it succeeded pretty well, outselling the GameCube and capturing a good userbase in North America and, to a lesser extent, Europe. (It also gave us great games like Deathrow, Phantom Dust, Oddworld Stranger's Wrath, and a ton of high-quality PC ports, so I for one really don't mind.)
In other words, MS disrupted a potential Sony monopoly. This opened the door for the Wii to capture the hearts and minds of the gaming community, and for MS to latch on with its "Wii60" campaign. And it looks like it's been pretty successful so far. MS hasn't tried to compete with Nintendo, but they have procured ports of former big-name PS3 exclusives (DMC4, Assassin's Creed, GTA4), as well as the attention and support of Namco Bandai and, to a lesser extent, several other Japanese developers who see the system as a "doorway" into the American and European markets.
So, all in all, it's capitalism at its best, and gamers are reaping the rewards.
"'Casual games' are something the 'Game Industry' invented to explain away the Wii success instead of actually listening or looking at what Nintendo did. There is no 'casual strategy' from Nintendo. 'Accessible strategy', yes, but ‘casual gamers’ is just the 'Game Industry''s polite way of saying what they feel: 'retarded gamers'."
-Sean Malstrom
