The most obvious is that the Banggai with eggs in its mouth is a male. Beyond that the differences are very subtle and inconsistent. The adult Male Banggai will generally have a more substantial lower jaw line. Some say the banner on the dorsal is longer on the male but I've not seen that play out more than 50% of the time.
A technique I used when I was breeding Banggai was to place a fish known to be a male in a tank with the unknown fish. If they fight it's a male, if not it's a female. This, of course, only works for adult Banggai. This technique relies on what Oceandude mentioned earlier - two male Banggai do not get along.