If you can get a bullet of proper construction, delivered with enough velocity to ensure full penetration at any angle, you will prevail, regardless of caliber. You will prevail that is, as long the path of your bullet bisects what we refer to as the vitals, but generally mean the heart, lungs or central nervous system. Sounds simple, yet problems arise.
Varmint and match bullets sometimes find their way into big game rifles. Sometimes bullets fail to perform the way the designers intended. Sometimes our desire for high velocity exceeds the design parameters of the bullets we choose. Sometimes we miss.
With the new bullets that are now available, and with the success of hunters harvesting game with minor cartridges, I no longer believe caliber is an important consideration of the big game rifle. Some ideas die hard however - such as my belief that any bore size smaller than .308" is for a varmint rifle, and that X bullets are designed backwards.