Wow, now that is a million dollar question and just to let you know, I feel like the sailor that is being pushed on the wooden plank waiting for his execution to happen by answering but hey, I have an extensive background when it comes with working with steel so I think I can give this one a shot

I, myself, me and I alone want, did I already say "I" twice, have seen both types of edges and like both of them.
The one thing that comes into play when dealing with single bevel edge is make sure you choose a high quality head that is made of good material. Due to the fact that the edge is much thinner, you need a harder material to help prevent both edge curling, bending and or fracturing. To use one is a matter of personnal preference and believe me, you have to shoot them to see what they can do. Here are the two top single bevel broadhead manufacturers that I have had the opportunity to work with by using and testing their heads:
Red Feather Archery - Phoenix 150 grain
Alaska Bowhunting Supply - Massai 150 grain
When your talking about dual bevel broadheads, well, choose your pick because you have on this web site, as per with the single bevel broadheads, some of the top engineers in the world to deal with. I don't think you'll find any people on here that doesn't believe in this incredible industry and all are willing to help in anyway they can.
And now to throw a third category in the loop, you need to take a long hard look at the Atom broadheads. Matthew, the man behind this incredible technology is an encyclopedia of knowledge when it comes to how his bevels work.
Also, reality says some like and some don't like so its up to you to follow your instincts and please keep asking questions and don't be afraid to try things, that is what makes this place such a great place to be in and listen, enjoy yourself.
I hope no one will let that plank go cause I can't swim !!!!!!!!!!!!! LOL
In total respect of everyone participating on this web site.
Daniel