What advantages are there in mounting a butterfly bar with a drop instead of a rise?
One thing you can be absolutely sure is: despite handlebars are designed to work some pre-defined way, there is nothing wrong about using them in a very different or even opposite way if that's what suits you best. The only two pre-conditions to do it is that you actually know what you want, and you actually know the practical, subjective pros and cons of each position.

If I were in your situation, I would choose the best position given my current stem. If that didn't work, I would perhaps swap the stem for another one that puts the handlebar in a better position.

Notice, also, that each image you posted places the brake levers in different zones, and that is a "design parameter" which you should consider. Most probably you'll benefit from having the levers in the position you stay most the time, so that they are within reach in case of an emergency stop being needed.

Hope this helps!