I use both regularly. SoundHound is my go to by default but I use Shazam as a backup. Shazam is more successful normally but I like SoundHound more for whatever reason.

Switched to SoundHound a long time ago and have found it equally as good as Shazam. I have every song I "discover" automatically added to a Spotify playlist so I can check it out later.

I didn't find much difference in recognition capabilities between Shazam, SoundHound, and built-in recognition on Windows Phones.