Short-circuit current is the amount of short-circuit current the device can safely handle, so it should be greater than or equal to the short-circuit rating of the device protecting it. For example. If the GFCI has a
short-circuit current rating of 10 kA. Then the short-circuit protection device protecting it (likely a circuit breaker), should have a short-circuit rating less than or equal to 10kA.
Maximum interrupting capacity is the maximum amount of current the device can interrupt. This value should be greater than or equal to the overload protection provided by the device protecting it. For example. If the GFCI has a
maximum interrupting capacity rating of 20A. Then the overload protection device protecting it (likely a circuit breaker), should have an overload rating less than or equal to 20A.
As noted in the document cited by another answer.
“Short-circuit current rating” is not the same as “interrupting rating” and the two must not be confused.
National Electrical Code 2014
Chapter 1 General
Article 100 Definitions
Interrupting Rating. The highest current at rated voltage that a device is identified to interrupt under standard test conditions.
Short-Circuit Current Rating. The prospective symmetrical fault current at a nominal voltage to which an apparatus or system is able to be connected without sustaining damage exceeding defined acceptance criteria.
As for which device would "win the race"... At current levels high enough to cause an instantaneous trip in a circuit breaker, the breaker should react in less than one cycle (16.67 milliseconds). I'm not sure what the reaction time of a GFCI device is, but I'd suspect it's slower than that.
I'd also like to note that depending on the length of the circuit, and size of conductors. A short-circuit might not be as much current as you'd expect.