When choosing Quad V vs. Quad X as frame type, I can not see any differences in the configuration. The motor assignment and spin direction is the same, the PID parameters are the same (no special set of parameters, that would reflect the asymmetry).
So when I want to bring a frame with the following shape into the air with Copter 4.1, which frame type should I choose and what should be considered specifically in the configuration?
I would use X. I have built a few quad with no symmetrical frames/arms and tried V and X. In one case it seemed to lack Yaw authority with V compared to X. I know of an X8 that had longer rear arms than front and it wasn’t symmetrical (kind of V) and X worked fine.