That's a good question.
I've heard a few op-amp based DAC's from expensive soundcards to hybrid Chinese DACs like the much loved yulong d100 and concluded they all sounded pretty much the same -- given that they shared the same op-amp. It wasn't until I heard a W4S and PLIII discrete DACs that really changed my idea of sound quality. Having heard a couple dozen headphones on my various op-amp DAC's I wish now that I could go back and hear them all again. Therefore my opinion would be it is important to get a good DAC, all music starts at the source.
Then theres amps; The 600 Ohm DT880 doesn't do much for me on the likes of the d100, Zero and other solid-state amps, a high powered OTL tube amp and it's another story. I believe strongly in amp synergy, pairing the headphones up with the right amp is essential, it can make or break them. Ultimately a headphone will keep it's sound signature even driven from an iPod, but in the likes of the DT880 moving from solid-state to tube, the mids fill out, the bass has brilliant extension and impact, and the highs are now lush and listenable.
You don't have a bad setup by any means and could happily move onto any headphone you desire, the question is will the pairing be to your liking.