Chuck I think Charlie summed it up pretty well. As stated there are two issues at hand but I have a different take on it. One is safety (NEC), and the second is performance (voltage drop).
I work a lot with low voltage battery systems and have to use voltage drop rather than 310-15. Here is a great example. Requirement 12 volt DC, 15 amps load current, 50 feet 1-way wire distance, voltage drop not greater than 3%. 75 degree.
If I were to use NEC the MINIMUM SIZE conductor required is #14 AWG. However if I were to do that, the circuit would never work because with 15 amps and 50-feet 1-way distance voltage drop would be 32% or 8.2 volts at the load device. To get less than 3% voltage drop would require 1 AWG. With that said NEC allows me to use 1 AWG with a 15 amp load protected with a 20 amp DC breaker. The circuit is now both safe and functional.
NEC 310 does not assume any operating voltage, or voltage drop, only currents for safety. Take that same exact circuit except now lets use 120 volts and now that 14 AWG cable works and safe.
Now here is the evil twist which Charlie is talking about. Using voltage drop can get you in big trouble when using short distance at the higher voltages. Another example will clearly demonstrate this point. Lets now say 240 VAC, 200 amps, 5 feet 1-way, 3% or less voltage drop. Using the VD method tells you all you need is 14 AWG. Does that set off alarm bells? 14 AWG with 200 amps? NEC minimum requirement is 3/0.
As Charlie points out you use the larger of the two methods. With that said my take is NEC is always the minimum, unless VD dictates a larger conductor. Most installation do not have voltage drop requirement. NEC is minimum safety and does not take operation into consideration.