I don't use AudioGalaxy, and I'm not sure why you need an account with them to use their app. However I believe that AudioGalaxy and many similar music streaming apps are simply file servers. You must own the song as an MP3 or other music file format.
SoundWire is different: it captures and streams audio, it is not a file server. It uses a special protocol to minimize latency. That means you can use it to transmit any audio from your computer live to your phone, especially streaming audio services like Spotify and Grooveshark, or streaming video services like YouTube (audio portion). You can also stream microphone or line input from your computer directly to your phone, e.g. hook up turntables and stream a live DJ set.
I use Grooveshark or Spotify almost exclusively now for my music, nobody needs to collect huge music libraries these days...