Though shot placement is crucial and the 243 Winchester, or 223 Remington for that matter, will do the job, I like to err on the side of caliber/bullet weight when it comes to hunting medium game. But that's me.
For varmint use the smaller calibers really shine. 17 remington, 204 Ruger, 223 Remington, 22-250 Remington, 220 Swift, 243 Winchester, and 6mm Remington. The .22 and smaller calibers really aren't very adequate for medium game.
So it seems that since a compromise is in order the caliber ought to be midrange. 25-06 Remington is probably the better option as a dual purpose rifle.