Well with fish, if you catch it, you've very likely produced a major physiological stress response in the fish. No one is putting bullets into the spinal column or brains for instant kills of unstressed, unsuspecting fish like may be the case in hunting. Whatever stress hormones or metabolites that get produced during the time from the hook set to the net would, it stands to reason, be sort of locked into muscles and other just from the stress of the fight and that is often from a fatal build up of harmful metabolites. Any fish that gets consumed must have whatever flavor alterations that are caused by whatever stress hormones tissue of the fish if the person decides to harvest that fish at that moment. No doubt fish have a major physiological stress response to being caught. Some fish and some types of fish are especially prone to dying and stress metabolites that are produced during the process of being caught unless those substances are somehow removed by bleeding, otherwise decay into something else, or are somehow volatile and evaporate into the air. I guess if one puts the fish on ice and the fish slowly expires on ice that could result in a different mix of hormones and the like than an instant club blow to the head or knife slash to the neck. I've done the fish kill a lot of different ways and some types benefit from bleeding as far as flavor goes. I would rather fillet one that is almost frozen as cold flesh cuts easier than warm, at least with some types of fish.
As far as a stress free humane kill, hunting offers a much better shot at that scenario than fishing other than maybe spear fishing. Whatever anyone thinks about making a long distance shot at an other wise unsuspecting animal, the animal is under no stress when the bullet severs the spinal cord or enters the skull causing an virtually instant and pain free death. In fishing, the fish is being constrained and forcibly being directed against its will. It only can respond to attempt escape with whatever abilities it possesses. If one attributes anything like human perception, feelings and emotions to the fish then there is no way to rationalize that fishing is anything but inhumane, no matter if you catch and release or harvest, intentionally kill, the fish or how you go about the process of killing. "Hey dude, sorry for tricking you and then forcibly sticking that hook through your lip and dragging you through the water against your will, no hard feelings, right?" "BTW, I'll be here next week when the BWO hatch is going off and my flies are so dang good you won't know the difference from the real thing. That's not going to be a problem for you is it?"