This work explores the influence of harvesting on the competition outcome in the two-species competition model with logistic growth law and different dispersal strategies. Both species are harvested proportionally to their intrinsic growth, but the harvesting effort may be different for the two species. In the absence of harvesting, the two competitors may coexist, and one can apply such "small enough" harvesting rate that the state of coexistence is conserved. In the situation, when, in the absence of harvesting, one population may drive the other into extinction, by applying harvesting to the "successful" species one can guarantee survival to its competitor. We provide estimates on harvesting bounds that would lead to a desired outcome, be it competitive exclusion or coexistence. The analytical conclusions are supported by the numerical simulations and visualizations.