Rather than using a particular caliber to matchup with the game, it's better to concentrate on bullet construction / weight / speed first and caliber last.
Magnum velocities require tougher or heavier bullets than comparable standard calibers and hunters need to be careful when shooting light-skinned game with standard bullets (at magnum velocities) that work well at slower speeds.
For 300 Win Mag / WSM on deer, I suggest 180-gr. loads because they'll perform similar to 150-gr. to 165-gr. .308 cal. bullets at slower velocities.
Same principle with the 270 WSM versus the 270 Win - Going up one size bullet for the magnum's higher speed (i.e. 140-gr. or 150-gr.) will produce similar results as regular 270 Win 130-gr. bullets.