Sometimes, I'll put productivity on the back burner for what's fun. I don't always look for the most productive way to fish, rather what's enjoyable to me at the time. These methods do sometimes produce well.
There is no best way to catch trout, PERIOD. The only trout angler who consistently catches fish is one who has mastered all techniques. I have outfished fly fisherman on quality streams using lures, I have outfished spinfisherman using flies, and of course, outfished both types of fisherman plunking minnows. I think the best time to fly fish is when trout become more selective, and a skilled flyfisherman can catch plenty of fish. I think a good system is to start with spinning lures, using this method you can find fish more quickly. once you are positive of a good spot, drifting flies would probably clean out the spot. Also you could plunk a minnow. don't even bother flyfishing stocked trout though, any lure or bait will clean out the entire section of stream.