Out-vying can be described using various synonyms to express a similar sentiment. One synonym for out-vying is outdoing. It conveys the essence of surpassing or exceeding expectations, as well as being better than someone else in a particular task. Another synonym for out-vying is eclipsing. It suggests a sense of overshadowing or supplanting someone else's achievement, as well as being the main focus of attention. Yet another synonym for out-vying is outshining. It connotes the idea of being brighter or more impressive than what is customary, as well as being a benchmark for excellence. Overall, these synonyms help to express the idea of coming out on top.