I have used the Fiio E11 and it does a great job with my x11i's. Give just enough umph and the bass adjustments are great if you are listening to Mp3's or a streaming service (like rhapsody etc) that might not have optimum bitrates.
Seeing bwbike saying
ands Thai saying
I think this may be due to the impedance of the s4 being 18ohms vs the X10 being 50 ohms. Phones and ipods are much more easily driven w/o a amp at that level, hence a stronger sound.