Previously, I noted that Double Drive (DD) spinning wheels can go faster because they have two drive bands to transmit that power from the drive wheel to the flier assemble. However, you may not really need to go that fast.
If you do not have a real need for speed, “Do you want a DD spinning wheel?” I suggest, not likely.
With DD wheel, the ratio between differential rotation speed (DRS) strongly affects the kind of yarn that you spin. A set DRS can help you spin a very consistent yarn if you are working with the same kind of wool and want to spin miles and miles of the same kind of yarn (production spinning).
On the other hand, if you to work with different kinds of fibers/wools, or you want to spin a different kind of yarn, with a DD wheel you need to change the DRS. This means changing your bobbin or changing your flier whorl or both. If you want to spin different yarns with a DD wheel you need a whole set of bobbins and flier whorls.
Now, some of this can be done by working with a partially filled bobbin to fine tune DRS, and some can be done by adjusting belt tension. However, these steps only take you so far. If you do not have a bobbin/flier whorl combination to give you the DRS that you need for the yarn that you want to spin, you are going to have to fight your wheel for every inch of that yarn that you produce. This takes away from the joy of spinning. This is one reason that people have different DD wheels. Each has a (set of) different DRS, and thus different yarns that they spin easily.
DD wheels come with a very limited selection of bobbin/flier whorl combinations that allow the easy spinning of a very limited number of different yarns. If you have an Ashford Traddy with a (Fast) DD kit, you will find it easy to spin lace singles at about 5,000 ypp. However, spinning 11,200 ypp singles leads to cuss words that cannot be said in public – until you get the right whorl (custom made), and then it goes like butter on warm toast. (Oh, yes, it can be done, but it is not as easy as it is when you have the bobbin/flier whorl combination to produce the correct DRS for that yarn.) If you want to spin 22,400 ypp singles (easily), then you need a different (custom) bobbin/flier whorl combination. Thus, if I want to spin a new kind of yarn, I start by going into the shop and turning a new spinning bobbin that gives me the correct DRS for the yarn that I want to spin. And, when I am spinning ST, I put a lot of yarn on my spinning bobbin. When I am spinning DD, I stop and wind off frequently, because as the bobbin fills, my DRS changes.
Scotch tension (ST) on the other hand will allow you to produce almost any yarn that you want from almost any wool. Small changes in drafting technique, or treadle rate or brake tension are all that is required to easily produce a wide variety of yarns. Thus, Scotch tension is better for people that want to work with a variety of different wools/fibers to produce a variety of different yarns. The downside of ST is that it has lower limits on speed and it is harder to produce a very consistent yarn.
The virtues of DD are ease of producing a consistent yarn very rapidly. The vices of DD are the extreme difficulty of producing yarns for which you do not have an appropriate bobbin/flier combination to produce the correct DRS, and the difficulty of obtaining appropriate bobbin/flier combinations for specialty or unique yarns (particularly for old wheels.)