The first one was plenty powerful enough for Windows (it was just a Pentium 3 700 MHz computer in a little box), but Microsoft certainly wasn't going to make a version of Windows that would run on it. They could, but they won't. And you can't because the source code isn't available (and the EULA legally bars you from reverse engineering it).
Linux, on the otherhand, being "free" software (free as in liberty, not free as in beer) includes the Source Code so users are free (and enabled) to create their own X-Box friendly versions of Linux. And they did. Right away. Really, especially when they first came out, the X-Box was a pretty nice computer for the price (since MS was selling them at a loss). It was a great way to get a cheap second CPU.
As far as Linux on the new XBOX. It'll probably happen. There's an entire community of Linux nerds just waiting to get their hands on it and start porting code. It will most likely be protected better than the first version, but that only makes it take longer, not impossible. The XBOX 360 hardware is essentially just a beefed-up Apple PowerMac G5 with a Graphics card on steroids. It's built using a 3-core PowerPC processor (all the Developer Kits for the XBOX -- what you use to program and test your game when you're building it before the unit itself is available -- are actually 2 PowerMac G5 workstations linked together). I know it's weird, but this did put Microsoft in the strange position of handing out Apple computers to their deveopment partners.
There is already a version of Linux (Yellow Dog) that runs on Apple G5's, so it's not a huge stretch to assume that they'll be porting it to the 360. The major obsticle will probably be dealing with the ATI graphics card component of the XBOX 360, which was built exclusively for the system and isn't extremely "PC-like". I seriously doubt that this will be a major hurdle though. ATI may not yet have any PC cards released that use similar technology, but they will, and when they do they'll release Linux and OSX drivers, and then the nerds will have the hooks they need (assuming they haven't already reverse engineered it anyway).
Of course, if you do it, you won't be able to access the XBOX live feature...
That's probably MS's biggest plan to protect the 360 from user-mods becoming mainstream. Unlike the original, they are now giving away a stripped-down XBOX live subscription free with the unit. They're hoping that people won't want to give up this feature to get some mods (which can potentially allow you to play illegitimate copies of games). Of course, the "freebie" XBOX Live subscription won't let you play multiplayer games online (it will be used for auto-patching, chat, and a BBS/WebForum type system), so that value is debatable. Either way, since installing Linux on the XBOX disables it's game playing capability by definition, I don't think this will be a major factor for the Linux-mod community to worry about. It will just be a cool, cheap way to get what will be the most powerful Linux box you can buy (at least for a little bit -- PCs will catch up quickly).
As far as the PS3... The Cell processor architecture could actually make it take a bit longer for ports to come out. However, the Cell is IBM's baby, and IBM is certainly Linux friendly (and currently developing a Cell-friendly version of Linux for their server business I'm sure). Luckily, the rest of the PS3 is very PC-like, so shouldn't pose a signifigant engineering challenge. Oh, and yes, the BluRay discs will be copy protected, but Sony has every intention of selling BluRay burners for the PC market (that's what the whole BluRay vs. HD DVD thing is about). I wouldn't put a lot of faith in their copy protection scheme. The one devised for DVDs worked
so well after all.