3. Very good. No major differences I've noticed between the One and S4 with headphones or BT. I turn off the Beats EQ anyways. BT Audio is very good. I stream to both my Audi and BMW. Never had any problems.
Actually the HTC one does have better audio reproduction, but the S4 is certainly no slouch. But from an audiophile the One produces better results.
I've compared both extensively, and yes we do actually have an audio recording studio and therefore have tested on very expensive studio speakers.
As for headphones,
Well those specific brands of headphones I have both the Klipsch S4i and then bought the S4a just for Android support. I should not have bothered.
Just so you know the support for them on Android is rubbish compared to iOS..., button presses / remote control doesn't work properly on either device. Even installing Klipsch headphone control doesn't male them work properly. You may get one press to register, the next time it will fail.
I even tried an alternative headphone control application and same problem.
The only Jays I have are the Jays + and they sound good with either device! just don't expect remote to work. (However as your Jays are BT you should be OK. BT remote support works grand on either device)....