Here's some stuff from GSMArena
Audio quality
Both smartphones did greatly in our dedicated audio quality test. Last week when we reviewed the HTC One we found it to have the best audio output of any smartphone we have tested over the past few years, but the Samsung Galaxy S4 didn't go down without a fight.
In fact, we were shocked to find out that the Samsung flagship had a cleaner output than the HTC smartphone. While both are perfect when attached to an active external amplifier, the Galaxy S4 remained just as great when we plugged in a pair of headphones, while the HTC One took a hit to its stereo crosstalk.
Still, it's a difference that's very hard to detect without lab equipment, so for purposes practical the two are on par. What is not so hard to hear is the difference in volume levels - the HTC One is notably louder than the Samsung Galaxy S4 in both test scenarios.
And here go the results so you can see for yourselves.
TestFrequency responseNoise levelDynamic rangeTHDIMD + NoiseStereo crosstalk
HTC One+0.11, -0.20-82.782.70.00230.026-80.9
HTC One (headphones attached)+0.02, -0.32-82.482.30.00450.057-68.3
Samsung Galaxy S4+0.25, -0.16-82.582.40.00330.023-81.5
Samsung Galaxy S4 (headphones attached)+0.27, -0.15-82.382.20.00530.029-79.5
The HTC One is one of the best DACs they have ever tested. The SGS4 is close to comparable than it. They mentioned that there's more power in the HTC One. It might be a tad more crisp possibly due to an amplifier someone mentioned earlier. But they are still comparable. So the DACs still might be on par.
But note that Supercurio doesn't agree witht he way GSMArena performs their test.
Still a mystery to me.