For me it all depends on hand position on the bars (lever is at the stem on my bullhorns) and proximity to an incident. If I'm far enough away I can move my hand I will use it, else, I'll just use whatever strength/technique I can to get the job done without it. The reasoning/judgement I use when I make these calls I can't explain, it just happens. Often my priority isn't necessarily stopping, it's just avoiding a collision - so it can heavily depend.
In non-emergencies, I alternate based on feeling/preference whether I'll resist or just rest and use the brake.