The two models are not exclusive, and can work together, although they are not necessarily the same thing. In a runaway process, one organism can select other "good" or "bad" (related to fitness) traits along with the favored trait in a mate.
Mate choice, in which members of one sex (usually females) choose mates on the basis of particular characteristics of the other sex. Usually, females tend to be more choosy. Why should this be? Two types of fitness benefits (direct and indirect) are though to drive the evolutionary mechanisms of mate choice. In case of direct benefit, mate choice by females increases the fitness by getting material benefits, including nuptial gift (the gifts that male animals transfer to females during courtship and mating), increased territory quality or parental care.
Mate choice by females in some species occurs even in which males provide no material benefits (i.e. no direct benefits). Mate choice of this short arises to get indirect benefits which increase the genetic fitness for the offspring. Three theories have been proposed to explain the mating behaviour of females:
Healthy mate theory
Female prefer trait that is indicative of male’s good health so that females (and offspring) can avoid contagious diseases and parasites.
Good genes theory
Female prefer trait that is indicative of male’s survival ability so that offspring will inherit the good genes for increased survival ability.
Runaway selection theory
Female prefer trait that is sexually attractive so that offspring inherit the trait that makes them sexually attractive.