The RAZR HD is a better phone overall. Way better battery life, better/bigger screen (although I think the one s screen is better calibrated), RGB NLED (and much better placement), SD slot, NFC.
Camera is much better on the S though.
Design/build is subjective. Both will have great perceived quality
Software is subjective. The razr hd software is very much stock android but with a few additional features.
Audio quality is more or less the same.