So I had the chance to finally look into this a bit.
This seems to be an issue with vertex weighting. Basically a character has a skeleton with joints, and each joint is weighted to control specific vertexes on a mesh.
To test everything I'm using DOA5&6 model extractions that I found on deviantart.
There are two neck joints on DOA5&6 models: a lower and upper neck joint.
DOA5 Eliot and Hayate on top and DOA6 Jann Lee and Diego on the bottom.
Notice also how the models have a seam on the neck. This is because the head and body are technically separate from each other, having a cut off point around the center of the neck. You can kind of see the seems if you look really closely when you view the models in game. I'm going to call these "Body" and "Head." (As a side note, holy crap DOA 6 models have a ton a bones for their faces)
What interesting/weird about the way these models distribute vertex weighting is that the lower neck joint is weighted in such a way that its twists only on the Body part of the neck mesh. The Upper neck joint twists both the Body and Head part of the neck mesh.
Notice above when I've twisted the neck using the neck lower joint the Head mesh has no deformation. This gives off an natural look because the bottom half of the neck is twisting but the upper part looks exactly the same.
On the bottom when I've twisted the neck using the neck upper joint, both the Body and Head mesh twist together giving a more natural look.
So it seems that the problem here is that in DOA6 models rely only on the neck lower joint instead of the neck upper joint (or a combination of the two as it probably was in DOA5). As such, if the neck is turned at an extreme angle your going to see a really weird protrusion on the neck.
Another issue here is that it the vertex weighting in DOA6 seems to be a little sloppy. This in combination with the technically higher-poly/more detailed model (plus the games higher targeted resolution) only makes the little mistakes more noticeable.
Edit:
Okay, I'm also noticing another thing. The way DOA5 cuts off the Body from the Head seems to be a little more intelligently thought out.
Notice how in DOA5 the seam is lower in the front and higher in the back while in DOA6 the seam looks more like a clean cut. I've noticed this allows the twist in the neck to look more natural on the DOA5 characters when using the neck lower joint, even though the Head mesh isn't twisting.
It's a little change that seems harmless, which is probably why it was overlooked, but it has a weird impact on the overall look once implemented.