Some wounds may be best treated by blood stopping agents, such as deep penetrating wounds that are bleeding profusely and don't lend themselves to being stopped by a tourniquet. If you don't have blood stopping agents (or you have a sponge type that won't fit in the wound) you may need to pack gauze into the wound instead.

Other wounds may be best treated with a tourniquet, such as a lost limb.

A pressure bandage might not work given the wounded person's position; for example you may not be able to apply the pressure bandage without extricating the victim but the bleed is such that treatment can't wait for extrication.

Don't use tourniquets for head wounds. Otherwise I don't think there's a one-size-fits-all answer to your question.