What Ohm headphones? 32, 250 or 600?

Tricky question that!
On one hand, we tend to want a very low source impedance and a very high input impedance so that the voltage is that what transfers the information. And that works well for lots of cases, and to a point it can apply to headphones, I suppose, but it is not the same thing.

Headphones, and loudspeakers, require power, not voltage, to change that changing voltage back to physical motion, and then pressure changes in the air. And for maximum power transfer we want the source impedance to equal the input impedance, at which point we do suffer a 3 dB power loss (silly laws of physics!)
 
If you increase the impedance of the headphones you will draw less current, which may mean you'll use less power, or it may not<G>. And if you lower the impedance of the headphones you are going to start using a LOT of current, and a lot of power. And it may, or may not, get louder.
 
Sorry, but this is where things land squarely in the land of "it depends". It depends on the design of the headphones. It depends on the design of the output stage driving the headphones. It depends on your definition of "loud".

If you know a lot about whatever device will be driving the headphones then you can start to make an educated choice. If you are using a lot of different headphone amplifiers then the 250 Ohm version might be the best choice overall, even if it is not the best choice for any specific device.

How was that for muddying the water?

wst3: Thanks this is helpful.  "for maximum power transfer we want the source impedance to equal the input impedance"
 
Paul P: thanks for checking the UR 44 manual - i don't think I would have spotted that reference.
 
This would suggest the 32 or possibly the 250 if I wanted some flexibility to use with other kit (assuming other studio kit has a higher impedance... which is pure supposition on my side).
 
Putting the loudness considerations to one side for a moment, would there be any difference in sound quality between 32 and 250? (ignoring the fact that we tend to think louder sounds better)
thanks again guys.

Some research turned this up. Hope it might shed some light:
 
http://nwavguy.blogspot.com.au/2011/02/headphone-impedance-explained.html
 
If I were to spend a reasonable sum on quality headphones I would be inclined to invest almost a similar amount in a quality headphone amplifier and they do make them. They have proper output stages that can handle range of voltages and currents and be able to extra the best performance over a wider range of impedances.  Compared to the basic headphone output jack on your interface or mixer etc which may not be fully equipped to do that.
 
Might give you some idea:
 
http://www.wirerealm.com/guides/top-10-best-headphone-amplifiers
 
https://www.whathifi.com/products/accessories/headphone-amps
 
https://www.aussiehifi.com.au/head-fi/headphone-amplifiers
 
The Hi Fi world is one place to look for headphone amps but they can be over priced as well. There are still lower priced options too and these would all be better than your mixer or interface basic headphone out.  A decent headphone amp will actually make your existing headphones sound better. 

I got a pair of DT-990 Pro 250 Ohms a few weeks ago.

They work equally well connected to my RME UFX headphone outlets, iPad headphone socket and MacBook. No problems at all. They are maybe slightly louder than my old Sennheiser HD-25s which I think are 32Ohm. Whatever, there's no shortage of volume at all. Not too bad for letting outside noise in either for open backed, though they leak enough out that using them for tracking close to a mic could be a problem.

They 990s are supported by Sonarworks and Waves NLS if flattening their frequency response is important to you.