Pro Hunter = Flat base
Game King = Boat Tail
The Pro Hunter is your general purpose "Hunting bullet" and does that job very well with adequate expansion and seldom over penetrates.
The Game King is a design similar to the Match King, and is also a great hunting bullet. It tends to stabilize a little better than the Pro Hunter because of the design, and is better suited for long range hunting distances.
It may have changed a bit over the years, but the Pro Hunter has a slightly thinner jacket than the Game King at one time.
Either will suit your hunting needs very well. I'd use the one that is most accurate in your rifle.