I used some Sennheiser HD280PROs for years (from at least 2005 to a few months ago) and they're nice studio monitor headphones, but very "flat" sounding, and the range of frequencies could be better (tops out in the 20KHz range, like 25KHz or something). 64 ohms impedance.
Now I use Audio-Technica ATH-A900 headphones, and they're very nice. Range of frequencies is up to 40KHz+ and the impedance is slightly lower (at 40 ohms) - probably just lowered enough to improve battery life on things without destroying their sound.
Volume in headphones (at the ranges you'd want to listen to) isn't tied to impedance, but the quality of the sound is. Probably more
detail than just volume, however: pushing up the volume won't give you static-filled noise.
Here is some reading on that issue; the author doesn't mention headphones specifically, but you get the idea.
Now, ignoring the balance of source to load (mentioned in the link above) for a moment...
Higher impedance phones can deliver detailed sound across a wide range of volumes, but high impedance phones suck more power, making them bad choices for plugging straight into most consumer devices (and they drain batteries faster). Plugging it into a weak source will give you thin, weak sound.
Low impedance phones are good for portable music players and most low-end decks and the like. Plugging it into a strong source will give you exaggerated bass and other nastiness.
Personally, I would go for whatever matches the situation you're using, but if (like me) you're using lower-power sources more often, you might as well go with a headphones that has consumer-level impedance. Just a wild guess that'll work nicer most of the time for you. Whenever I run into distortion, I dial back the volume a bit.
I would also pay some attention to the hertz rating, as a wider range is always nicer. Switching to a different pair of 'phones may take some getting used to (and some adjustment - head-fi.org has some guides, which I haven't bothered with, on tuning frequencies on your audio devices to your ears by using pink noise).
There are some equally important characteristics that don't seem to be marketed as such. The HD280PRO is a very flat headphone, i.e. the sound is usually right around your ears. Not terribly exciting. The ATH-A900s, on the other hand, have very detailed sound (that I blame on the ancient computer speaker I'm using as a ghetto amp - that because the front-panel imput on my PC case was shabby, heh), and just as important the sound on the A900s is also much grander in scale - stereo separation is very nice, and puts you in the middle of the sound. I've read a review where somebody noted that some old recordings' stereo separation sounded exaggerated with these, but I've felt nothing of the sort.
Finally, the closed vs. open headphone debate. Even open headphones will leak less noise than speakers (for obvious reasons), so if said neighbors are on the other side of a wall you might get away with some nice open headphones. I bought my ATH-A900 headphones in part because they were a closed design, so I can listen to stuff without annoying people, but these actually leak some sound - and don't block as much as the HD280PROs did.
Final thought: Save your ears; get some decent equipment that will render detailed sound BEFORE you have to push the volume up. You can always get a new pair of headphones, but you'll have those ears for years to come.
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