Based upon my eight years of experience and 46 years of fly fishing with fly rod and reel, I would say that it would be most advantageous to fish a fly rod and reel in the following situations:
1. The target species is over 20"
2. The water is running high and moving fast and there is a need to bounce nymphs on the bottom.
3.There is a need to present a fly that is out of reach/out of wading distance of a Tenkara presentation.
For all other trout fishing situations, and occasionally, even some of the above, tenkara is a more effective means of presenting flies, consistently drawing strikes and landing fish.
By "tenkara" I mean the use of tenkara fly rods, lines, tippets and techniques (casting, fly manipulation/dance). This includes traditional Japanese tenkara, whereby an angler fishes reverse hackle kebari flies. It would also include using tenkara rods and lines to make the most precise, delicate and life-like presentation of western flies.
I have caught 100s of cutthroat (both resident and sea-run) and rainbow trout, as large as 20". I've also caught brown trout and grayling in Croatia and Spain. Twice, I hooked steelhead on tenkara but could not land them. These were times that I wished that I had a rod and reel.
I am not totally dismissing fly fishing with rod, reel and fly line. I love to make a long, precise cast to distant rising fish using dries or soft-hackle emergers, but still, day to day, I find tenkara to be my weapon of choice.