I've always used the iPhone headphone output and I have never found any issues with sound quality. Funny how some people here are offering advice when they clearly have no idea what they are talking about.
Beats... EQ... lol. Anything done in post processing cannot be used to define sound quality. Wolfson DAC? Please, a DAC hardly makes any difference at all.
The only thing you should focus on is output impedance, and the impedance of your headphones. The output impedance should be as close to zero as possible, and your headphone impedance should be as low as possible to avoid the need to drive the op-amp to distortion levels, or the need for an external amplifier.
If the output impedance is high, then you starting having issues. Your headphone impedance either needs to match or be higher (and you may have to use an external amplifier). If your output impedance is higher than your headphone impedance, you start to completely change the frequency response of your headphones.
Just for everyone's information, iPods and iPhones have use good op-amps with output impedance under 5 ohms, which makes them sound accurate with just about any headphone (although high impedance headphones may need external amplification). So if your sound quality is shit out of your iPhone, it's clearly your headphones.
So OP, next time you think something doesn't sound right, find out the output impedance of the device you are using, and the impedance of your headphones, and you'll have your answer. The former should ALWAYS be lower.