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?