Eyrie is built on Echonest servers and music database. Yes, for the sole purpose of music recognition it is good if the song is inside Echonest.
Soundwave is built on the same servers that SoundHound uses. And it has extra features.
Soundwave is a paid app, while Eyrie ia a free alternative. Everybody is free to choose what to use.
Shazam is built on their own server. I'm really sorry this didn't work out.
In terms of quality and accuracy, I'd say SoundHound servers are the best, then Echonest and then Shazam.
I analyzed all the code, you can take my word on this.
Point is, use what you can.