I'm not sure what the Xbox 360's operating system is based on. Since it's produced by Microsoft, I doubt it is Linux.
I also doubt that the PS3 will come with any standard Linux variant, it's probably modified extensively to suit them.
I'm sure the 360's OS is related to Windows in some way. The original (Xbox OS) was based on Windows 2000, but heavily modified to a point where it was barely recognizable. Considering that the Xbox 360 uses a tri-dual-core-PowerPC-processor architecture, I doubt that the kernel is even close to being the same. It also uses non-traditional shader pipelines and allows the memory to be partitioned as the developer sees fit (as opposed to giving you memory and saying "that's what you get"). So a lot of things are much different than your traditional PC game programming, and I'm not sure that Windows would translate well.
As for the PS3 having Linux.... Isn't the point of Linux to bring Unix to x86 (or isn't that its roots)? PS3 uses the Core processor, in this case a system with 7 symmetric cores (with one redundant) and the PowerPC-driver processor.
PS3 will feature free online as well. That's pretty awesome.
I haven't heard a thing about this, which is odd considering I've been following this generation pretty closely (since I was a 360 early adopter). They seem to be putting a lot of eggs in one basket if it's true; I can't imagine they want to lose *that* much money on *every* PS3 console. They might be offering a free basic service like Xbox 360 Live Silver.
