My experience is, use if and only if needed. The less gear the better. Definitely standing if needed. In fact, I dont think running is even allowed in hunters. Never use martingale in equitation classes
Standing are more "conventional" in the lower levels because they are more restricting, but running martingales are used in higher levels. My suggestion is if you need it, use it, if you don't need it, don't use it. Judges are more drawn to performance and turnout than tack choices.