But thats more 90% theory...
Me x3: Things like headphones, phones, DACs, amps, soundcards, TVs, exist thanks to scientific and engineering theories.
I am pretty sure, a 1200€+ planar magnetic headphone with low impedance will sound way more precise than a 300 Ohm HD 600/650.
You can pretty much completely ignore the Impedance of a headphone, as it alone gives you Zero information about anything. You will have to try, and view the headphone as a whole.
Me x3: Look, it's not as simple as you think.
Driving a low impedance planar magnetic headphone with an amp with 10 ohm output impedance is also less than ideal, but a planar has flat impedance across the spectrum so the frequency response is not altered when driven with an amp that has a slightly high output impedance.
Here you can see the Audeze LCD-2 Rev 2 (flat) impedance plot
http://www.innerfidelity.com/images/AudezeLCD2Rev2.pdf
On the other hand, the impedance of the dynamic headphones discussed here has a bump in the mid bass so when plugged into an amp that provide poor damping factor the mid bass is boosted and loses some control.
Here you can see the Fidelio X2 impedance plot
http://www.innerfidelity.com/images/PhilipsFidelioX2.pdf
For example, my smartphones drives my 250 Ohm T90 so loud, that i can't endure above 13/15 volume on my smartphone. (with NO external amp or anything)
Me x3: Nothing wrong about that, the Beyerdynamic T90 is a very easy load, similar to the HD600.
They need around 0,22 Vrms to sound at 90 dB, and since they are high impedance headphones they drain very little current from the amp.
So, just blindly saying no to X2, and yes to HD 600 just because of a Number on the specsheet, is pretty wrong. It CAN work, but it could also be just the opposite.
Me x3: Impedance plot is not a number. The simple physics facts behind how the output impedance can alter the frequency response of a headphone support my comment which is far from a blind suggestion.
This is a pretty interesting and simple article that you may find useful (3 pages):
http://www.innerfidelity.com/content/meridian-explorer-case-study-effects-output-impedance
But anyway, we can just name you good headphones, that might fit. Its still YOUR turn to test them yourself