Single and double drive wheels should not be confused with single or double treadle wheels, they're two different things. A single drive wheel can have two treadles and a double drive wheel can have one treadle. A single treadle wheel has one foot pedal (treadle) while a double treadle has two.
A double drive however is where the drive band is looped in two and goes over both the flyer and bobbin whorl turning them both at the same time. The flyer whorl however is smaller than the bobbin whorl so it turns a little faster than the bobbin, winding on.
In a single drive wheel, the drive band goes over only either the bobbin or flyer with an adjustable cord or band (the brake band) going over the other one.
A single drive wheel where the flyer is being driven and where the brake band is over the bobbin is called scotch tension.
A single drive wheel where the bobbin is being driven and where the brake band is over the flyer is either called bobbin lead or irish tension.
Most Single drive wheels are scotch tension though all louets with the exception of the victoria are bobbin lead.
The advantage of double drive is that they like spinning even yarn. Since both the bobbin and flyer are being driven at different speeds, the takeup is smoother and it almost forces the spinner to spin even. The downsides are that the takeup tension can't really be adjusted: you can loosen or tighten the drive band a bit, but loosen it too much and it won't work. It's also hard to spin anything other than what the wheel wants to spin, which is thin and even.
The Advantage of single drive is that the tension is adjustable, so you can set it light when spinning slippery or short staple fibers and give it more takeup when spinning bulky. Single drive wheels are much more novelty yarn friendly. It also tends to be easier to change the bobbins on a single drive wheel than it is on a double drive.
The disadvantages are that it sometimes takes alot of fiddling to get the right tension and that single drive wheels don't force you to spin even like double drive wheels do, so it takes more practice to spin even on one.
All double drive wheels can technically be converted to single drive by affixing either a rubber band or a cord with a spring on the end, over the bobbin, but that doesn't mean that all double drive wheels should be converted. I personally wouldn't convert one unless the manufacturer gives you the option.
While ashford does sell a kit to convert a single drive traditional to double drive, AFAIK they are the only ones to do so.
I know that there are alot of people who loathe it but I personally have a single drive single treadle ashford traditional and I like it.