Sometimes they expire differently. Both harvests have minimal meat damage. Well, where I hunt elk is open too, and I have a bull and cow and a black bear tag. I do not carry different rifles for each game. The bottom-line it boils down to a personal choice of rifle set-up/chambering/load, intended purpose, and the "NUT" behind the trigger's ability, competency, and experience. PRACTICE, PRACTICE, PRACTICE ...
Yes, there is always the possibility of a bullet wandering (Murphy's Law) in another direction but let us NOT turn this into an ethical hunting issue as this is NOT what this thread is about. Let's move on.