9mm vs .40 is a chliche , that after all the shouting boils down to somewhere between "whichever you prefer" and "flip a coin" .
As far as safety in carrying thru brush and around obsticals , a securely holstered is safer than a long gun with typical sling setups , or carried by hand(s).
The first post wasn't clear as to the context of "bring along on hunting trips" . Primary hunting tool for big game ? The proverbial coup de grace on downed but not deceased big game ? Small game hunting ? Plinking during lull in hunting ? Night time security in camp ?
For legality for hunting a particular species , consult your state's game regulations , they vary widely.