Price Point. First to motion control. Family friendly, and it was hyped better.
When the 360 came out, the RROD held a number of people back. When the PS3 came out, the massive price, and difficult-to-program for(at the time) RISC Cell architecture slowed its sales considerably. Nintendo's better reliability, and easy to program PPC SDK gave the damn thing a huge running start.
360 also had the problem of pushing a format war through a console, via an add-on drive, but going with an end of life design to push HD-DVD. Big mistake IMO.
In the end, the consumer won. More options and variety.