As I understand it.
It appears that the Steambox is more of a concept and a brand rather than an actual product. The Xi3 is a Steambox device but it's not
THE Steambox as the Steambox doesn't exist as a singular device. I believe that the Xi3 was released by Valve and will be apart of a whole range of their own "Steambox devices". There will be other companies working on devices independently that would carry the brand. The Shield however can apparently work as a Steambox but I'm unaware if they carry the "brand".
To have a Steambox "brand" the device would have to obviously adhere to some design philosophies such as being non-closed software and would have certain hardware standards. Having Steam installed on the device as default would be mandatory I'd wager.
This could very much be the death knoll for console monopolies, which I can't say I'll shed a tear for. It's pretty exciting stuff but I don't think it will affect a lot of the Bay12 community. PC gamers won't see much of a change apart from a shift from restrictive console game design to a more open and pc-focused market. There will hopefully be a lot of fun toys to play with in the future which company competition should help to keep prices low.
The biggest concern here is the monopolisation of the digital PC market by Steam. This is actually not as big problem as only having console closed markets as it appears that all Steambox devices are open and new operating systems can be installed, meaning Valve cannot force people to buy games off Steam or any services of their's in the future. There is the worry that the shear size and brute force of Steam could drown out other competitors though.
We may see Steam prices increase if Valve decides subsidies are needed for their devices to keep prices low. This is unlikely now but if there isn't any other real competition it is a possibility.
Prices will be the determiner if the Steambox concept will work or not. If the Xi3 is truly 1000 USD as some people have speculated from the hardware then I doubt it will be able to penetrate the market at all.
If you mean PS3, Xbox and DS by that, I'm betting PS3. Mainly because the DS is a portable system + pok駑on games, the Xbox has a few cool things (like being able to use the controllers on computers) and the PS3 has the least going for it.
I see Nintendo dying out personally. Xbox has Microsoft backing which isn't going anywhere soon, Playstation has the Sony network. Nintendo has been struggling to find their niche for a long time. The DS is woefully outdated in both hardware and utility by these new products. The WiiU just doesn't have enough going for it and being released in between console cycles will likely castrate it later. All Nintendo will be able to do is milk old franchises (as they've been already doing) until consumers just get bored with them.