Redoing the classic PIMETA design, eh? Both parts are quite decent choices, but obviously the devil is in the details and implementation.
The main drawback of this specific buffer is the quite large voltage drop if large amounts of current are sourced - so do remember that this won't really work to source 250 mA if you give it 3.7V or 5V supply. This is typically not an issue in headphone loads, as high current low impedance headphones are usually sensitive enough. Do note that the result will be current mode drive - balanced armatures respond differently to voltage and current drive and voltage is the more common mode in headphone amps.
Note that V/I converters need a matching I/V converter and amplifier. It makes no sense to use these for short cable runs - they're made for PA systems.