Maybe you guys can help. I am ordering a new pair of brogans, and "rough out" seems to be the style.....which would you recommend? Which is more authentic?

Here is a link from the Authentic Campaigner Forums on this very subject which might be of interest to you:
http://www.authentic-campaigner.com/forum/showthread.php?t=13286&highlight=rough+out+brogans%26quot%3B%26quot%3B

Sir:

Without a doubt, flesh side out aka "rough out" was the correct construction for the Army contract shoe. Civilian shoes were most often lined, either in cotton drill or fair kid skin, but "smooth out and unlined" was also known in the civilian market.

Keep in mind that military contract, especially low bid military contract, are cheaper versions of things in the civilian market. Whereever they could cut costs and get by the inspectors was fair game.

Army shoes and ones issued to Confederate Prisoners were often the same shoes produced for slaves and "negroes"(in the north for shipment south). Confederate Prisoners were noted to be issued "Inspected and Condemned" Federal contract items, which were items that were purchased by the government, but found to be unfit for field service.

To make a long story short, "rough out" is a comparatively cheaper shoe of the period.