Blu-Ray was not a better format than HD-DVD
But it won anyway for a few simple reasons
1) The HD-DVD on X360 was an additional $200 add-on expense
2) The Blu-Ray on PS3 was included in every model and much cheaper than stand-alone Blu-Ray players
3) Content
Sony owns a significant portfolio of Hollywood movie studios
Sony made deals with others like Warner Bros and Paramount for timed exclusive Blu-Ray only for their HD movie library
So ultimately it was about Content
It is always about Content... and for Games Blu-Ray hasn't really been that useful because it is much slower than DVD so to allow the game to load/run fast anyway they put the same data on multiple parts of the same disk. It also makes developers stupid about optimizing and not using good compression techniques which again help the games load faster.
Case in point
The massive game world of Skyrim on X360 fits on a single DVD Disk or it fits on the much larger Blu-Ray disk but runs more poorly.
I do like that Blu-Rays are extremely resilient and scratch resistant.
