How does the Samsung Galaxy S3 "fall short" to be specific? I've personally found all of the Galaxy S-line of phones to always have a very enjoyable sound quality whenever the headphone amplifier is presented with a relatively easy (not too low impedance), high efficiency load. That implies the DAC in the phone is completely fine and has resolution and clarity to sound good when used correctly and either using a headphone amplifier, or taking the internal amplifier's limitations into account.
To be brutally honest, if I was the thread starter, I would most likely get some more mobile/efficient set of headphones that isolate a bit, rather than trying to mask out environmental distractions by needing a mobile amplifier with a massive output wattage into a high impedance and low efficiency load. But since that was not the answer you are looking for, if you absolutely need to use the current headphones, then as recommended earlier, the FiiO E12 would offer you way more output with a selectable bass boost. If you need even more bass, you can use the internal EQ of the phone/tablet/whatever.
Also, if you would all be so kind at least try to bother with the spelling and punctuation, you're not really adding much to the collective intelligence quota.
Sources: I own the Samsung Galaxy S Wifi, Samsung Galaxy S, Samsung Galaxy S3.
Another thing I might want to implore you to pay attention to, is that you're considering these devices for mobile usage, no? It's nothing short of obvious, that when mobile you're hardly going to enjoy the luxury of quietness and no distractions (commuting, traffic, people, other sources of city noise). Without a silent environment, it's very much likely that the better DAC/amp you would be getting (with minute differences in resolution and presentation at best), is not going to sound any different when you're squeezing yourself through a crowd or sitting in a resonating bus. The absolutely massive difference you felt you heard at home when testing your new gear, is going to be much less impressive when a car is honking next to you or someone can't shut their baby up.
EDIT: wait, the Fostex headphone amplifier has only 80 mW@32Ω, whereas your FiiO E07K Andes has 220mW@32Ω. I feel like you're way lost about what you're looking for. Throwing $600 at an amplifier is going to fix nothing if the amplifier doesn't give what you wanted, that is more power.