Just earphone quality and the included buds well the HTC one is better. Boom sound enhancement with beats works great over the headphones and brings music alive. The S4 has adapt sound which after setting up enhances audio through earphones but overall result isn't same but still good nether the less.
Camera on the HTC one was why I left the device. Camera is important to me and whilst the HTC one is passable for instagram/twitter etc. It just can't compete with its higher megapixel rival.
S4 has a great camera but I just never loved the phone. There was always something hovering over it that prevented me from ever truly loving it whether it was a feeling that the s-apps were half baked on it, to occasional stutters in performance.
The note 3 gives a android as smooth experience as the HTC one but with camera of the S4. The S-Apps like s - planner just feel natural and at home on the bigger device and the scrapbook in / action memos and s - notes likewise work great on the bigger device and with the s-pen. The OS is buttery and never falters and im actually enjoying touchwiz (bar some GUI aesthetic choices).
For me the HTC one was brilliant sound, great screen, decent battery life but sub par and frustrating camera.
S4 was great camera surrounded by a Ho hum experience that just never gelled together in any coherent manner leaving my experience with it shallow.
Note 3 so far has been sublime in all areas, great camera, great software features, fantastic battery life.