And I'm the same as Don, only the opposite. I use my trusty Badger 100LG DA brush for just about everything BUT fine lines, then I pull out my even trustier Badger 200-20 "Detail" brush. I find the ability to dial in the line width much easier to do than trying to control the width with a trigger. I find the SA to be slightly more time consuming to clean, and I mean slightly, maybe an additional two minutes in time.
In reality, there is very little difference between the airbrushes. The head assembly and air valves are the same, and only the needle (length only), trigger and body are different. A flawed analogy is to think about them as transmissions, the DA is equivalent to an automatic (I can change gears easily just by moving the stick) and the SA is like a manual (clutch first, then change). Either will let you drive the car, and once you've become used to them, shifting becomes second nature, so you can concentrate on the drive.
One HUGE difference is that the DA lets you change line width easily, so you can do a flood coat on one section and then hit a tiny spot without changing anything but your finger position. With a SA, you would have to stop, adjust the line width, test on a piece of scrap, adjust some more and continue.
Judicious shopping can let you afford both, I paid $75 for my 100LG and $40 for my 200-20, so pretty much the same as buying two or three kits.
Otherwise Don is correct about practice, and I would like to add that you will need to practice.