Update:
I've been reading some more about using the DT770 (80 Ohm) without an amplifier, and understood that they're not THAT hard to drive, so I decided to give it a go and ordered them the same night. Got them yesterday, and I must say I really like the sound (although I do realize they need quite a lot time to burn in).
When listening to metal(core) I get that deep bass, without getting too boomy and the bass drums and bass guitar "clogging up" (don't know how else to describe it) the rest of the instruments. Bu when listening to rap with fat bass I do get that BOOM! So it's exactly what I was looking for.
Now about the impedance... it's clearly quieter than my AKG K512MKII and Philips SPH8500, wich are both 32Ohm, but it still goes loud enough. With my mp3 player's volume set to max (30) it's even a tad too loud to be listening for longer periods. When set to 25, I find the volume ideal. However, it doesn't sound that impressive anymore... it misses the "fullness" (again, I don't know how else to call it... soundstage??).
At the moment I don't have the money for the Fiio e11 (not even thinking about the e6 anymore), but I could get it next month, maybe even for my birthday
However, before I decide getting the e11, I'd like to know if it would give me that "fullness" I mentioned earlier on lower volumes. My logic says yes, but I just want to be sure... so what improvement could I expect?