Bore size I'd no substitute for shot placement and
Power is no substitute for bullet performance
I shot a cape buffalo 15 yards with a 416 Rigby with a 410gr Woodleigh solid across the right front shoulder and on through the heart. It turned and ran 80 yards, collapsed and bellowed.
I shot a cape buffalo at 15 yards with my drilling's 9.3X74R barrel with a 286gr Woodleigh solid across the right front shoulder and on through the heart. It turned and ran 50 yards, collapsed and bellowed.
I'm sure a 30-06 with 220gr solids would have had the same results, given the same shot placement.