There aren't a whole lot of manufacturers who offer high-impedance, high-fidelity headphones. However, when you get up into the stratosphere of high-end cans, they're nearly all high-impedance.
Beyerdynamics' excellent
DT880 (semi-open) is one of the few mid-priced hi-z models, and it's actually available in 3 impedances, including 600 ohms. (The company also makes a well-regarded headphone amplifier with switchable output impedance - for a couple grand!.)
Impedance matching is nearly as important for headphones as for speakers in general. You wouldn't hook up 4-ohm speakers to your 16-ohm P.A. amplifier and expect optimal performance. (You might even blow up the amp!) Like speakers, headphones are current-driven devices. The lower their impedance, the greater the current required of the amplifier. High-impedance headphones are more efficient, with more windings (smaller wire) in their voice coils so that it takes less current to generate the magnetic field. So yes, higher-impedance cans might be a better match for your interface's headphone amp.
The downside is that if you ever want to use those hi-z headphones with your portable music player or smartphone, they might not perform as well because portable devices operate at lower voltages.