What advantages are there in mounting a butterfly bar with a drop instead of a rise? I own a tourer with a butterfly bar mounted with the near flats rising.  This puts the far flats rising towards the outside of my wrists.  I have, however, seen butterfly bars mounted so that compared to the stem the near flats drop.  This would put my far flats falling towards the outside of my wrists (a position I suspect I may like better.  But I'm having difficulty finding comparative evaluations of mounting butterfly bars in these manners.

Mounted rising: http://memberfiles.freewebs.com/74/22/55522274/photos/velocelestes-R20/R20top.JPG

Mounted dropping: http://sheldonbrown.com/deakins/images/flatandtrek.jpg
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!