My preference is and always will be single backhand, there isn't a right or wrong, choose what you are comfortable with.
This is my take on single backhand, (for the Pro's) most of them that had single backhands had a more well rounded game. They had more variety and disguise when using a single handed backhand, people with single backhands, tend to have better 'slice' shots and approach shots when coming to the net, also they tend to have better volleys.
If you are talking about overall success of single hander's there are more World No:1 players that were single handed players and there were double backhanded.
Double backhand pro's: Very solid ball striking when on, seldom you have shanks ala Federer....,you can create sharper angles due to strength of extra arm,double backhands are especially good for return of serve, Agassi was a prime example, now Murray, Djoker are excellent return of servers.....
Cons:I rarely seen a double hander consistently attack the net, most double handers are extremely fit people who prefer to stay at baseline and win from there, double hander's need an extra step in order to set up.
For social tennis , I think nowadays the 2 hander is 75-80% popular mostly due to the fact you see results faster, student feel more satisfied, however 30-45% of them from this 75-80% will just a mediocre 2 hander, other coaches I have seen that teach a 2 hander mainly tell the student to 'loop' the ball over, ala 70's style moonball.........
To be 100% honest most of the strong players I have encountered 75% of them are single handed players, when I meet a 2 hander, I will go for really good high topspin, if the 2 hander is comfortable with this, I go to 'slice' shots, deep penetrating slice, to dinky floaters, to short angled slice shots, if I bring the 2 hander to the net will test his volley skills kau kau, esp test his backhand smash....