The E10 is a DAC so it will give you the best sound from your PC out of the other Fiio products. The E11 is a portable amp, but would sound good from your PC also. However I don't think you can use the E11 while charging. A few M50 owners on here will tell you they don't even need any amp or anything. I strongly disagree. I guess it all depends on what kind of sound you prefer.
I'm not trying to work against you here - I've come to understand you're a big fan of the amp you have. So the following is not meant as anything but discussion. I still don't get how a run of the mill amp can improve on the sound. Say you have this setup:
iPhone -> amp -> headphones
then, the iPhone will output sound in its way due to its DAC. If you then plug that straight into the headphones, some of its frequencies will be emphasized over others due to the headphones frequency response - some headphones are heavier on bass etc - the main point with an amp is when you have "professional" headphones that have a high input impedance that needs more power to have the same loudness, and your iPhone (etc) doesn't have enough output power to play the material loud enough.
The idea that an amp can make something sound better, just from the way it works (not including tube amps that give certain inexorable qualities to the things it amplifies), it can never make anything sound better, because it takes the input voltage and amplifies it. What does that mean technically? The variation of voltage is what gives a tone. If the voltage in on a headphone variates as a sine wave from 1 mV to -1 mV 440 times per second, you'll have a 440Hz tone.
Now put that tone (-1 to 1mV) and put it through an amp. The amp will merely take every "momentary" voltage and multiply it (there's no momentary, because it's not discrete, since we're talking analogue electronics) - so that means when we measure 0.5mV on the original input, it'll be upped to, say, 1mV if you have a 2x amplification. This means the input will variate from -2 to 2mV, but still at 440Hz. The tone is exactly the same, but it just has a bigger voltage variation. An ideal amplification does exactly that, always. Ideal here means to describe an electrical system in which all conditions are ideal, and everything works in a theoretical ideal - people say tube amps are better, not because they're the closest to ideal, but because the way tubes work works its mojo on the stuff it amplifies, and thus make it sound more "organic" and such.
Often you'll hear the argument that you need an amp to properly drive you headphones. This doesn't mean that lower volumes will be driven better, because low volume is still low volume. What it means is that the headphones were made to work in a certain loudness - it's possible that frequency response works in a non-linear way for the various frequencies at various input power - that means if something is played at a low volume, the bass may drop off because it's simply lower than the mids at such a low volume.
Then take this scenario. You plug your headphones into your iPhone (or what have you), and you crank the volume all the way up. The way it sounds now should be exactly the same as dropping the volume to 50% and then getting the last loudness by amplifying it by 2x, because an amplifier should merely amplify.
If an amplifier does more than that, it changes the characteristics of the sound. This would be a nightmare amplifier to me. I want as neutral sounding tonal characteristics as possible. If my amp changes the frequency response, ie adding more bass, I wouldn't be happy. Even if the intent was that the ones making it know that most headphones drop off in certain frequencies at certain volumes and compensate, it'd still be a completely individual thing for each and every headphone, so unless it was made for my headphones, it's not doing the right thing, to me at least. Of course, if you feel the M50s aren't bass heavy enough and your amp rectifies that, then that's great, but my ideal world is one where sound is input directly into the brain, so we can hear it exactly the way it was produced. I fear most professional productions out there produce their music in a way that suits the characteristics of the most popular headphones, meaning someone like me with pretty neutral headphones will be left back with a song not sounding the way it was intended. Then again, I know house and rap overdoes its bass already, so I don't see the point of having headphones that further overdoes that.
This complicates things, but I have to take things at face value and say that the way something comes out of a studio is the way it was meant to be heard un-equalized. Headphones that are heavy on bass works against this, and I don't feel I'm in any position to say that "my favourite band doesn't know how to mix, and it needs more bass" - which is why I'm sticking to neutral.
All the above is pretty much rambling about the theoretical aspects of amplifications. Maybe there's some mojo to most amps out there that can make something sound better for some reason? In that case, I'd love to hear how and what. Let's not forget that an amp cannot improve clarity, as clarity often comes from build quality of the headphones, and the actual weight of the drivers in the elements, and how fast they can move back and forth to produce a sound - faster is better since they can stop exactly when it should, not some milliseconds later.
Also, it scares me how loud some people listen to music. I have a pair of 250 Ohm headphones that are loud enough with my iPhone. Sure, there are some crowded situations where it's a tad too little, but amp'ing 32 Ohm M50s due to lack of loudness? No wonder people are ruining their ears at a young age.
