Found this forum/thread whilst researching what DAC the Samsung Galaxy S4 had and couldn't resist giving my 2c. inc. GST worth...
I have both a iPhone 4S and Samsung Galaxy S4 (Australian version) - the sound quality on the Samsung sucks. It's thin, aneamic, lacks bass, lacks volume and is listless and lifeless. Whilst the iPhone 4S isn't perfect, it's far better than the Samsung.
I've been an audiophile since the mid 90s, my home system is worth around 30k AUD. I use both Sony MDR-V55 headphones on the run, and Audeze LCD2 or Sennheiser HD540 Gold References when at home. I have a pretty damn good idea on how to assess devices for sound quality issues.
Buying headphones that aren't neutral or flat to fix issues with the Samsung's issues is not fixing the problem. It's a bandaid fix. you don't make a right with 2 wrongs.
Since I plan to move from the iPhone to the Samsung, and sound quality is lacking, I've just lashed out on a AK120 II as a dedicated DAP. I'll use the phone as a phone etc.
For those wanting great sound quality at a reasonable price, the Fiio x3 (or x5) will do everything that you want - supporting up to 24 bit 192khz, flac, ape etc, and even DSD file playback. They'll eat your phones for breakfast and then some.
Dave