I've moved to Portland from Northern California, and in visiting a new dojo I saw that their strike style was vastly different from what I'm used to. The strike there describes an arc, like the belly of a 'D' when seen from the side, as opposed to the whiplash, 'L' shaped strike that I'm used to seeing (and have had pounded into me). Any comments on the respective strengths/weaknesses of these two styles?
I think you are saying that at the new dojo, they raise their swords all the way back over their heads so they are facing behind them?
And in your old dojo, they would raise their swords vertical, and the bring them down vigorously?
And in both cases the end of the cut is parallel to the ground?
Well different groups do it different ways, and everybody has a schpiel about why this way or that way is better. Even classical sword schools.
Some people will pooh-poo the "D" shaped cut, because there is not usually a good combative argument for hauling your sword all the way back there. You are going to lose time, and you have to make it rise before it can fall onto your target. Some schools will tell you that any further back than 45 degrees is bad.
But you get a nice range of motion and if your swordwork involves keeping your shoulders relaxed (if it is any good at all it will be mostly about keeping your shoulders relaxed), you can feel what happens way back there.
Iaido people do cuts like this. But it is not unheard of in classical kenjutsu either, to bring the sword to at least parallel to the ground - so your opponent cannot see it.
The other cut you are describing, the "L" shape, what might be a problem there is your description of it as a "whiplash." You can get something like a whiplash by putting lots of upper arm and shoulder into your cuts. That's really really bad. But if your swordwork is more along the lines of "just let the sword fall straight down" that is fine stuff. I just don't usually get a whiplash that way.
If you have your shoulders tight, you will see the blade of your sword do a crazy zig-zag on its way down. That is easier to see and feel with a bigger, broader "D" shaped cut IMO.