Its all about preference. Hell, the most famous elephant hunter of all time used a 7mm mauser to kill 1,011 elephants. 175gr FMJ going 2400 fps. Talk about less than ideal.
I assume you are talking about Bell: he shot elephants with pin point accuracy with a "brain shot". He also shot birds in flight with a rifle. That's not a preference - it's skilled. (The only reason he used the 7mm Mauser was the reliability of available ammo).
Disregard above if you can perform a "brain shot" on a deer; 22 short will do just fine.