Nvidia has a clear advantage in price
Not if you already own a PC and an Xbox! I have no use for the Nvidia gear, already have a PC, and am considering picking up an Xbox One around Christmas if there's a good bundle with a 1TB model.
Still, there is an obvious downside to using this streaming service as opposed to dedicated hardware. Video footage consumes loads of bandwidth, and if you are playing online, you will likely see performance drops.
BS alert! Modern wired/wireless networks have gobs of bandwidth, if you're streaming from your XB1 to your PC you're not even relying on your internet, just the local network. If you're streaming outside your network to twitch or whatever, you'll need decent internet but that's nothing new.