Missed this thread earlier - my experience:
Did a blind and volume-matched test with the One and S4 (i9505 international version with the same DAC as the one). Listened on 12 and 16ohm IEMs and 32ohm cans.
First interesting thing was that the Samsung stock player is noticeably louder than PowerAMP (not yet tested other third party players). Around 10dB louder if PowerAMP has direct volume control off and ~5dB louder if PowerAMP is using direct volume control. Since we wanted to use the same player in both devices we had to drop the HTC One volume down three notches for them to match closely (only one step to match with the S4 stock player).
Turned off Beats on the One.
Noted with interest that when blinding was removed and we could see which phone we favoured in our notes we both preferred the S4 sound over the One overall, better instrument separation and clarity, less fatiguing and harsh. Generally preferred the bass on the One, although the One was quite boomy. There was one MAJOR problem with the S4 though - crackling with prominent low bass frequencies. This was absent on the T5p at 32ohm, noticeable on the 16ohm IEMs, and very noticeable on the 12ohm IEMs. I ripped the 12ohm ones from my ears after about 5s, the crackling made them unbearable. If this is output impedance related as it appears to be this would put the S4 (i9505) output impedance somewhere in the 4-8ohm range, making it impossible to recommend to anyone using more sensitive IEMs.
EDIT: I see current could be an issue too.
Edited by NZtechfreak - 5/9/13 at 9:20pm