The method of breeding depends on the estimation of the heritability of the desired trait, hence the high heritability traits ( important additive gene effect ) can be improved by phenotypic selection.
In the case, there are large difference between broad and narrow heritability that refers to the importance of the dominance action gene, can be improved by mating system
What kind of trait would you like to breed. I have seen aggressive chicken in tel-Aviv. usually aggression goes with other good qualities. Here is from the rodent perspective: