Ghrumpy

"Much stiffer" what? "More power transfer" where?

The only thing a Chubhub really does differently is transfer power across the hub barrel, so both flanges are involved in transmitting drive torque to the rim. A traditional small-barrel hub transfers very little torque from the drive side to the non-drive side. Of course such a large barrel requires large flanges, unless you want to make the spoke hole circle smaller than the barrel diameter. (It's been done....)

Does it make any difference? @TejanoTrackie is on the right track (pun intended.) Spoke crossing pattern makes a lot of difference. Spoke thickness makes a lot of difference. Rim stiffness makes a lot of difference.
Flanges make little if any measurable difference in wheel stiffness, and probably no difference you can feel.

Elastic flex of some materials induces fatigue and failure. But whether elastic flex of a bike and its components is "wasted" energy is not necessarily true. While it may seem axiomatic, humans are not machines, and clearly a certain amount of "flex" can allow for the human body to perform better. Think of mountain bike suspension. Anyone remember when that was considered "inefficient?"
If that flex makes it difficult to control the bicycle, then it's not a good thing. But that's an entirely different issue.