It looks like they copied all the features of Sleep Cycle (and the companion app, Power Nap), made it look a little nicer, and tacked a few on like audio recording and achievements. The hardest comparison to make would be in the actually quality and accuracy of the tracking. I wouldn't even know where to start for that comparison.

I tried to make the move from Sleep Cycle to Pillow and found myself going back to SC. Pillow may be prettier but it doesn't seem as usable as SC.