@blackhawk
i've personally heard audio from a sony walkman mp3, ipod nano 1st gen, ipod nano 2nd gen, ipod classic, direct output from laptop, direct output from my home receiver (amp), cell phone, and from various cd players and other audio devices.
the headphones i have used ranged from $10 gummy in-ears, $15 jvc in-ears, $20 sony in ears, $50 ipod in-ears, $20 generic over-ears, $200 bose over-ears, and my $150 audiotechnica over-ear studio phones.
from my experience i can tell you that a good set of headphones, or even just a different model of equal value headphones can make a world of difference in terms of what you hear. i will agree that the amp in mp3 players is on the weak side, but in most cases is more than enough to get the sound you want. a portable amp can help but in some cases can introduce more background noise than its worth.
in general the isolating in-ear headphones can generate more bass than ipod style phones and non-enclosing over-ear designs. as far as sound quality goes, it does vary by model. i like the ipod phones myself but since i replaced the headphones often because of gunk-up and wear-out i was using cheapies and replacing them every two months.
currently i'm using the very model i suggested, the audio technica studio phones, with my ipod classic almost every single day at work. there is no loss of bass or quality whether i'm plugged in to my mp3 or laptop. the headphones DO sound better when i'm plugged into my receiver but that is to be expected. the quality increase isnt enough to make me want to buy a portable amp as its just not worth it.
i keep the EQ fairly level with just a very slight kick up for bass and its at a comfortable level. the bass has more than enough kick for stuff like dubstep, hip-hop and rock while staying clear enough to not muddle lyrics and high tones.
the biggest step to take is to get a good pair of headphones. sure, any headphones would sound better with an amp provided the background noise doesnt increase too much. however, the amount you gain compared to the money you spend just doesnt compare with what you can get through buying a great pair of headphones.
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as for your iphone audio quality:
perhaps i summed it up with what i said above. yes you would see an increase with an amp, but a better pair of headphones might have given you an even larger increase.