We have a pound mutt (we think lab-shephard mix), that was abused and abandoned. He's lived the feral life for a while, and knows he has it good. He has blind faith in us as the pack leaders.
He's no proper hunting dog, but he uses his nose, and knows what a gun is.
He will run anything he can smell or see, and attempt to tree it or push it to me, classic hammer/anvil. Just yesterday he got a doe 15 yards from me, and was already off on another from the herd. He won't listen that its not deer season, nor can I hunt deer with him. So they got passed. Got me a squirrel out of the brush yesterday. Killed it too, where my shot pattern hadn't.
He'll run into the brush and spook up small game, and if close enough to hear/see it fall, he'll retrieve it. He'll defend our kill too.
He will run through 6" of snow when it's below zero to the point his paws are cracking and bleeding, to get us game (not doing that again, sorry bud). Come in my house and you better hope I shoot you before he gets to ya.
No luck on birds as we don't have any local. I don't want him going deaf so I wouldn't bring him to blind hunt waterfowl or dove.
He's training our elkhound-shepard mix pup to hunt. She's picking it up pretty good.
In my little knowledge/experience, the breed doesn't matter as much as their desire to hunt/kill and be a part of your pack. I'll take a smart mutt over a two thousand dollar papered idiot. We also don't believe in dogs that live locked up in a kennel/run. Ours are part of the family/pack. They eat wild game with us. They sleep under our bed.
That said, obviously breeds are that way by design. Hence why we got an elkhound mix. We wanted a hunter, and took the alpha of the litter. She works pretty good as an alarm dog. You just can't cram enough guard into 35lbs to be useful though it's not for her lack of trying. I think she's going to do great on rabbit once season opens. I've seen her outrun bunnies in the yard. Might not even have to shoot, she'll probably just kill them herself.