I shot 3 whitetails last year with my 30-06 handloads of the 165 Remington Core-Lokt spitzer at a modest 2650-2700 fps muzzle velocity. 2 shot at 75 and 135 yds with high shoulder shots dropped instantly into fetal position with all 4 legs pulled up to torso, instant kills. The third was shot at around 60 yds just behind the shoulder and took two jumps before expiring 25 yds from where shot, about 3 seconds after impact.
Mike is absolutely correct as to quick kills: shot placement #1, and bullet construction #2. Caliber makes less difference now than 20 or more years ago before the advent of so many premium bullets. The original premium, the Nosler Partition, is still a great killer over a wide spectrum of velocities, which cannot be said of all the premium bullets out there. Many of the newer designs require high velocity to keep from acting more or less like a solid. The Partition does not. It opens nicely at standard velocities and penetrates deeply.