@fearmonkey - Whilst both Xbox One and Playstation 4 utilize the cloud, they do so in different ways. The XBO uses it to add power to console (albeit, you need to be connected) whereas Gaikai is used for streaming games, not game textures etc. Also, Sony's isn't running straight from the off, its taking 'til 2014 if I am not mistaken.
That said, not sure I am a fan of the cloud. Whilst the XBO's Azure cloud will them the edge power-wise over the PS4, not everyone will want their console constantly connected in order to play a game. Some games may outright require it, which would be a problem for those whose internet may go down. I dunno, if the internet didn't have the potential to be temperamental, then this might be a more welcome idea. I mean, personally, I haven't been without internet in a long time, but for those that might have been, if they focus on this cloud, it might mean certain games are rendered unplayable altogether. Personally, I think power in the box might have been a safer route, like what Sony took. If we were comparing them power-wise without the cloud, Sony's wins hands down.
I also like the idea of backwards compatibility through Gaikai, since I never owned a Playstation console before, this appeals to me as it means I may get to play all the games I missed out on with being an Xbox owner. I mean, I've already played all the games I wanted to this gen for Xbox, but the removal of backwards compatibility seems like an odd move. Some wont have played them, and that's where Sony wins this one, despite not having Gaikai until 2014
tl;dr - both use the idea of the cloud, but in a vastly different way.