... but nothing conclusive.
I'm 98% sure that the movement on the left (single piece) is more recent. I say that after comparing various Langematik Perpetual movements. The Langematik Perpetual has been around for much longer than the Annual Calendar and has the same basic movement. The older Langematik Perpetual movements looked like the one on the right, with the small sub-bridge (if that's what it's called) at the top. The movement in every white gold/black dial Langematik Perpetual that I've seen looks like the movement on the left, and that particular model (WG/black dial) was introduced just a few years ago. That's why I think the one on the left is newer (and of course, we could just look at the movement serial numbers too). I wouldn't conclude that the more recent version is necessarily better, though, and I definitely wouldn't let the movement version influence my purchasing decision. Lange may have made the change for some other reason (e.g., perhaps it's just easier to service or manufacture).
Also, I thought I answered you several days ago in that other forum, but I see that my post never went though -- odd.