.308 will do all you need it to. You really can't compare the 2 because of weight difference in bullets and diameter. For coyote's, I would choose the .243. One better would be the 6XC. You get the same performance as the .243 w/ less powder. It will also be easier on barrels than the .243. The nice thing with either is there ability to shoot 105-115 grain bullets really well. Heck both would be good whitetail rounds to 800yds with good shot placement.
I like the .308, but it has it's limitations and need to be considered. For a strict coyote rifle, the .243 will be the better of the two options.
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