From what I have learned in college and from researching the subject for years, about 60 - 70% of fish that are deeply hooked survive when the hook is cut, as long as the fish is not heavily bleeding. Most so called stainless steel hooks do not rust out rapidly, but the slow breakdown produces caustic chemicals that help release the hook.
How often a fish swallows a hook is not really related to what you are fishing with, but HOW you fish it. If you choose to fish bait, use very sharp hooks and keep the rod in your hands, and in rivers use the drift method. Done this way, 90% of the fish should be hooked in the mouth, lip, or jaw. And if 10% of these fish were deeply hooked, and if all fish that swallowed a hook died, the mortality would be 10%, or about 5% higher than flies or lures. However if half of all fish that swallow the hook survive, your mortality rate is 5%, the same as flies or lures. This is why for the most part I do not support flies and lures only regulations, except on small heavily fished rivers or small heavily fished lakes. They are basically not needed on any large body of water regardless of pressure.
Usually when properly fishing bait, 90 - 95% of fish you hook should be hooked in the mouth and not the esophagus or stomach.
Just regardless of what you are fishing, when the fish has the bait, set the hook.
Tyler