Females prefer courtship over competitiveness, findings of a study making it official (at least in the horned beetle world), and size of the mandibles don't matter either.

Female mate choice and male-male competition are the typical mechanisms of sexual selection. However, these two mechanisms do not always favour the same males.
Male horned beetles have enlarged lower jaws – or mandibles – used to fight rivals, and those with larger mandibles do have a mating advantage when there is direct male-male competition. But until now, it has not been clear whether the females actually prefer these highly competitive males.
After conducting experiments with hundreds of the insects, the researchers show that female choice targets male courtship rather than mandible size, and that the two traits are not physically or genetically correlated.
Professor Dave Hosken, of the Centre for Ecology and Conservation at the University of Exeter's Penryn Campus, said: "A major finding of this study was that the most attractive males, those most preferred by females, were not the highly competitive males with large mandibles. This is despite the fact these fighter males enjoy significant mating advantages when in direct competition for females. Instead, females prefer to mate with males that court more. This shows that choice and competition favour different traits."
Source-Eurekalert