I have tried desperately to protect my $120 investment in a Fiio E12 Mont Blanc amp to use to "help" my iPod Touch 5G drive my Grado PS 500 headphones. But in fact, the amplifier makes not a hill of beans of difference... the sound is absolutely awesome from the line out (or from the Lightening to 30 pin to DAC to line out) connector... indistinguishable between with- and without-amp configurations.
And I SO wanted to hear an improvement with the amp... well, maybe with some other headphones (the Grado PS500s, at 32 ohms input impedance, are right within the space for which the iPod Touch 5G output was designed!)
When I had the Fiio E11 I felt even worse because I noticed that instead of improving the sound over the headphone out it actually colored the sound and added artifacts.
I do not want to seem like an audiofile but after owning or demoing the Fiio E11, E12 and the JDS Labs C5, I came to the conclusion that unless you are willing to spend at least $300-400 on a portable amp the headphone out is the best way to go for audio quality.