After many years of hunting, I have become convinced that "Enough Gun" has much less to do with the size of the caliber than it does with the shooters ability to place a single, well aimed first shot into the vital zone of the prey, all while using a bullet of sufficient structure and momentum to penetrate deep enough to kill the animal. The size of the hole, be it 6mm, 7mm, 30cal or 375cal has much less to do with the results as long as the hunter knows when and where to place that first shot.
While there might be more room for error with the larger, heavier calibers, they come with their own set of handicaps such as more recoil, and more bullet drop on longer shots.
Spend the necessary time with your rifle and chosen caliber to be "Expert" in its field use and choose bullets of high quality. There are more good bullets out there these days than bad. Just don't choose a frangible varmint bullet to shoot a Kudu and you should be OK. Don't choose a solid or FMJ to shoot deer. If you want more "Bang-Flop" type kills, then go bigger and faster. If you do not mind doing some minor tracking then the choice may be less critical. Just be ethical and avoid taking shots so far out that the bullet is not delivering sufficient energy for a good kill. Even if your marksmanship skills with allow such shots, they should not be taken. We are better hunters than that. For large game, I try to limit my shots to the range where the bullet arrives at a minimum of 2000fps using a heavy for caliber bullet.
i.e. For a 30-06 loaded with 180g Barnes TTSX that works out to about 400y. Not every hunter or rifle is able to deliver acceptable accuracy at that distance. From a bench or prone off of a rucksack, I can make such a shot at 400y but for hunting, shooting off sticks, I limit my shots to 300y to allow for those other variables and prefer to get within 200-250y whenever possible. I cannot think of many cases where I would have needed to shoot further. Possibly if out West on smaller game like Pronghorn.