I think the advantage of Tenkara is that you can manipulate the fly lifting and dapping it with greater accuracy than a cast with a shorter fly rod. What it comes down to, as it always does, is presentation.
Any advantage in fish catching must come down to the fact that in certain fishing situations a tenkara outfit presents the flies more easily and with greater precision than a standard outfit.
I just listened to a talk by George Daniel, author of Dynamic Nymphing, and a former member and coach of the US National Fly Fishing Team. He was in Madison, Wi this past weekend.
The question of tenkara came up, and he said he nymph fishes tenkara just like he does with his euronymphing set up. He uses a sighter and the same flies.
Here is a post about it on a Tenkara BB
Tenkara USA • View topic - George Daniel on Tenkara