Can I use an amp lie the fiio e11 with an android phone and still expect a similar increase in quality to an  mp3 player or ipod?  I'm new to amps and just confused about LOD and DAC

What is the difference in sound quality between the three types of headphones of similar value?

I'm looking for headphones to use withe my android phone and computer. I listen to various music types including rap, rock, pop etc. I'm not obsessed with bass and mostly want a pair of headphones with good overall sound quality. Its mostly for at home use but would be a plus if it could be...