Lorien When you say L and D are you meaning as Cliff said or:
L: The arms come down the center line of the body with the sword sort of vertical and the wrist "snap" out at the bottom of the cut. The classic Saito type shomen seen performed by a lot of aikidoka. See at 1:40 on the video below:
D: The hands and wrist "cast" out from the head and the sword is bought down almost in an elliptical motion. As seen in most Iai and Kendo: See 1:25 in this video :
The first I see as aikido training, building that extention from the centre for open hand technique, tanren training. As a sword cut itself the mechanics of the cut mean maximum extention and power of the cut occurs near the belt level. With the D cut the maximum speed and extension of the blade is at the forehead (shomen) of the opponent and the blade then slices back towards your belt.
Two different cuts for two different purposes. Not bad or good, different.
You'll see a lot of people when they have someone in front of them checking their range and practicing their distance, extend their arms and sword to the forehead as if they were doing the D shape cut. An interesting exercise have an uke stand in front of you and check your distance to their forehead by extending arms and the sword to the forehead. Then cut with the L cut slowly, if your uke is my shape you'll hit about the top of the belly, if uke is fitter about the bellybutton
Then without moving do the D cut and you'll strike shomen.