I think Desertdog gets at the heart of it. A good fisherman measures his satisfaction in fishing in terms besides number, length, and weight of fish. He gives as well as takes. I also think that anyone who actually cares how good a fisherman he is probably isn't very.
The ability to catch lots of fish or fish of many species in fresh and salt water also does not a good fisherman make. I know exceptional steelheaders who have never caught any or only a few salt water fish. But that is because they choose one sort of fishing over another. They would probably be equally good at fishing bonefish, tarpon, or marlin if they dedicated the same effort toward it.
Catching lots of fish or especially big fish isn't the mark of a good angler either. A passible fisherman can catch a lot of fish or big fish if those are what are around. A good angler is one who fishes 5 miles of river and catches two or three when there were no more than five in the entire stretch of river. Catching 5 or 10 when there are hundreds or thousands around is a nice catch, but not an impressive achievement.
A good angler is the one who catches the large and wise brown trout from under its extensive root wad holt, covered with overhanging vegetation, with conflicting currents moving multiple directions, and takes this trout in direct sunlight on a size 18 or smaller fly on 6X or lighter tippet. Catching a hundred steelhead is easy by comparison.
A good angler is one who gets an exceptional measure of satisfaction from fishing and all the ancillary activities that go along with it.
Sincerely,
Salmo g.