First advantage of ball diffs is that they are lighter than gear diffs, so less rotational inertia so the car accelerates and brakes faster. The most important place to lose weight in a car is in the drivetrain.
Secondly ball diffs are adjustable, but there are limits to the amount of adjustment in micro size diffs. If the track is very low grip you can loosen the ball diffs so they slip to reduce the amount of torque that gets to the wheels. The advanatge of slipping the ball diffs instead of a slipper clutch (if fitted) is that you can vary the amount of slip at each end of the car, enabling you to tune the amount of torque going to each end of the car to adjust the handling.
When running the diff loose but not slipping (or a gear diff) you get more steering off power turning into the corner, but you get less traction coming out of the corner. As the diffs are loose the wheels aren't fighting each other turning into the corner so you get better grip off power. A loose diff also means less traction under power so less acceleration out of the corner.
The advantage of tightening up a ball diff is traction. If the surface is a little slippery with a gear diff all the power goes to the wheel that slips, rather than the one that has grip. By running a ball diff slightly tighter it makes sure that power still goes to the other wheel when one of them slips, so you get better acceleration. By varying the amount of slip you can also adjust the amount of traction at each end of the car. For example if the buggy spins out under power setting the front diff a little tighter means the front wheels tend to pull the buggy out of the corner and therefore makes it more stable.
Using a tighter diff at the front the stiffer action means the wheels tend to fight each other turning in off power, so you get less steering which can be used to make the car more stable. Using tighter diffs means under power you get more traction as the tyres aren't allowed to slip, so better acceleration. An extreme example of this is in touring cars, with their front spool. Much better and more stable acceleration out of the corner but much less steering into and through the corner than running a diff, they get the cars to turn into the corners due to the slick tyres slipping on the tarmac which is why to run foams on carpet you have to replace the spool with a diff.
As for which is preferable for racing the ball diff is the preferred option, because you can set it as free as a gear diff if needed, but with the option of adjusting it to suit the track.
I also race my buggies indoors on carpet with more grip than I can possibly use, so traction isn't a problem. I have always run gear diffs in the Lazer ZX-R as the free diffs means it carries much more speed through the corners as the tyres aren't fighting each other, but as there is loads of grip I don't have to worry about any tyres slipping coming out of the corners. I would run ball diffs but getting the old Lazer diffs to be free enough while not slipping wasn't easy.
Running with a gear diff up front and a ball diff in the rear is a useful tuning aid, after all Tamiya sold buggies with that setup for years. The front ball diff gives better turn in and steering through the corner, with the rear ball diff helping traction coming out of the corner. You can get a similar effect with gear diffs by filling the rear one with Tamiya Anti Wear grease which stiffens up the diff action a lot.
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