Originally Posted by ProtegeManiac
1. Amplification is NOT the/your problem. The typical smartphone has around 5mW at 0.1% THD, maybe up to 15mW for some tablets, while the DX50 probably has well over 200mW at possibly even 0.01% THD,* which is not only 40x the power output but also at likely a lower distortion rating. The DX50 also has a dedicated amplifier section with bigger power capacitors (still tiny, but bigger than what phones have), so current performance is a lot better as well. The DX50 also has a lot more power than the E6. Given these figures and you think the G2 sounds much better, amplification specifically output power cannot possibly be the problem here.
*A guesstimate based on the Fiio X1 having around half the power of the X3, which in turn is comparable to the DX50
2. Frequency response. What makes the G2 sound better for you is very likely a matter of frequency response, and given your initial assumption is that the DX50 needs more power, it is very likely that the Ibasso DX50 has a more neutral response and the G2's software tunes the EQ to sound/seem like it has a very dynamic output (I am assuming you did not enable any EQ's on PowerAmp), usually done by boosting midrange frequencies down to the upper bass. This brings out the main range of music out a lot more, and particularly with the drums, they have a stronger "punch" or "kick" to them. If overdone however this can make it harder for the 5mW integrated chip on the smartphone to drive headphones/IEMs, as on dynamic drivers for example boosting lower frequencies (even the upper bass) tends to require more excursion from the drivers, which in turn requires more power and current. Since that does not happen, it's likely that along with an easy enough to drive headphone that you're using, and as with a factory setting, likely not overdone. AFAIK, a lot of software or other "collaboration" products tend to use such a trick, except for Beats Audio's negative application of similar principles, which AFAIK (as mentioned before in some threads here, not sure how accurate) when installed and enabled, does nothing; then if disabled but is left installed, applies EQ to make the disabled sound (and by inference, the smartphone or laptop without it) sound lame.
3. Headphone or IEM. What were you using with all of those? Sometimes it's harder to appreciate the benefits to better amplification unless you use a better headphone/IEM (or even speaker), which in some cases, their design might have resulted in other compromises with regard to how easily they can be driven (higher impedance, lower efficiency, wider impedance swings from nominal, etc).
4. Gain. Check the DX50's gain - if it is on low and for example you tried an E6 at high gain, you will mistake the latter for sounding "better," as long as THD doesn't really kick in.
5. EQ Settings. Also, you can use the DX50's EQ to mimic the same "dynamic" sound. Play around boosting frequencies from 70hz to 500khz primarily, then a bit less for above 500hz to around 8khz. Not sure what specific frequencies can be tuned but tweak within that range.