Thanks, Earbones. My IEMs are Dunu DN-1000s, which have an impedance of 10 ohms, and an efficiency of 98dB. Both of those numbers are fairly low among IEMs, and I'm finding that the Moto X doesn't drive them all that well. I get too little bass (which is where most of the energy should be going), and although the presentation is quite airy, notes are thinner and a bit less detailed than when they're driven by my Sansa Fuze, and dynamics seem poorer. When the phone is amped with a Headsix, it's quite good. But then, so is the Sansa, though the two sources sound really, really different.
If I'm understanding correctly, low-impedance 'phones are generally easier to easier to drive in that they require less voltage than high-impedance 'phones, but by the same token, they require more current. (I'm working off the explanation here: Headphone & Amp Impedance Questions? Find the answers here!). According to the 1/8 rule, which I read about someplace else, you want an output impedance no greater than 1/8 of the headphone impedance; in this case, that would be 1.125. I suspect that my phone's HO impedance is somewhere north of there, and the battery is not delivering enough current. The Fiios and iBassos have output impedances of <1 -- as does the Headsix -- while the AK series, if memory serves, are something like 4, which would be fine for driving 32 ohm 'phones.
If the Sony 88x has an impedance in the range of 1, I think it would probably drive the Dunus perfectly well. If not, I'd be better off going with a Fiio or iBasso or Hisound or whatever. I can use the Fuze/Headsix stack, which is tiny by amp stack standards, but two devices<2, when you add my phone, which is too curved to stack and use with the Headsix).
Sounds like you've a decision to make; whether to get a new phone with a better internal amp or a standalone player... Honestly, I'd go with a player if I were in your shoes. I know it's silly but I don't fully trust cellphones in terms of exactly how bad for people they may be... I don't generally plug my ears into them unless I've put them in airplane mode. So it's more convenient for me to run a player. Kind of a lame reason, I know, but I guess we all have our eccentricities.
Edited by Earbones - 4/23/14 at 1:11pm