i don't believe the seasoned hunting dog to be at a disadvantage from his quarry, on most occasions it will be the first time the rabbit/fox/deer etc has come into contact with a dog, the dog on the other hand at the very least will be doing this once a week during the season,the quarry may have "home turf" advantage as you put it, but the dog has vast experiance at the game.
"so surly in my mind there is the chance that that rabbit will get away am i right or wrong? so how is this the same as putting two dogs in a 15 ft ring to go toe to toe"
it is'nt the same,the rabbit WANTS to get