I've found Shazam and Soundhound to be pretty much identical in terms of accuracy when identifying music, however I tried monitoring each app's usage with 3G Watchdog but couldn't get a clear winner between the two, so the question remains:
Which app uses less data?
I looked at the answers for this question: [ How can I choose between Shazam and SoundHound? ], which compares the two, but no information .was provided on data usage.