I use rdio, and it's not the streaming that makes me keep paying them--it's the legal access to a mountainous library of most of the music I ever have a reason to give a listen to.
I will probably keep paying Rdio, but I also recognize that I am in a minority of listeners that constantly listens to new stuff.
Before this announcement, Rdio had a huge value proposition even for normal people: instant access to all the music in their collection from multiple devices. Now iTMS has the same offering, for less money, and with better integration into every platform normal people play music on.
Rdio will undoubtably be faster at delivering a "random song", that is, one that's not already downloaded to your device.
Often times I'll be somewhere remote and want to listen to an album I haven't listened to in months. Without having to download each file first, Rdio starts playing instantly.
I'd actually argue that now that Apple's trajectory wrt cloud music is pretty clear, Rdio and MOG probably are breathing a bit easier that they can fill a niche without worrying about iTMS just outright replacing them.