For thin skinned game, I would incline to the smaller caliber, assuming shots were to be taken in the open with little liklihood of intervening underbrush. 6.5 mm is a favorite of mine, and incidentally the minimum caliber for wild boar in some European countries. The .256 Newton, although long discontinued from production, lives on in cartridges like the 6.5 Remington Magnum, the 6.5-.284 and the 6.5-'06, plus the intriguing 6.5X64 Brenneke and 6.5X65 RWS.

For thick shinned game I would go in the opposite direction. Where the use of full jacketed bullets is concerned, I prefer the largest diameter bullet the shooter can comfortably and capably shoot.
This is why virtually all my thick skinned trophies were taken with caliber.500-.505". I feel that this caliber combines sufficient bullet weight with sufficient penetration without the risk of expending terminal energy on thin air, as a result of a bullet which exits the animal.