hot mop vs. torch down
Please check out "liquid applied ceramic roof coatings" at www.icc-astec.com (Michael Rubin 800 345 5306) they will direct you to a local applicator.
Both hot mop and asphalt (black) coatings attract and absorb heat from the sun.
White Ceramic coatings reflect radiant heat from the sun.
I have personally applied these coatings on many types of roofs, and am very impressed.
You'll be glad you did this research.
Good luck, & best regards, Brian Wood.
But to get to the original question, sorry to confuse you even more but there is a rubber type of membrane called EPDM that has taken over the majority of the flat roof market with good reason. It is my first choice to date. I recomend that ypou seek bids for it, too.
Torch down Modified roofing was developed to replace hot mop built up roofs in certain applications. Either material must be applied by a skilled team to give good service. But have numerous potential flaws but either can give you a fifteen year roof, if instsaled properly. They are comparable in my mind and the more important thing to consider is the references and reputation of the installer.