I think we can agree that for any desired amount of control surface travel (say 1"), there are any number of servo arm/control arm length combinations that will work.
It is easy to achieve zero linkage slop by using quality products like bolt-on swivel links and titanium pro-links. If you use z bends, soft metal rods that flex, and/or loose-fitting clevises, then you deserve what you get. However, if your linkage is sloppy anyway, then the shorter servo arm/longer control arm combination will result in less control surface movement.
Gear slop is not a factor. Regardless of how long your servo arm is, gear slop will result in the same amount of control surface movement for the desired amount of control surface travel you've chosen. Longer servo arm/shorter control arm means the servo arm connection point moves a lot but the control surface moves less. Short servo arm/long control arm means the servo arm connection doesn't move much but the control surface moves more. The net result is that the control surface moves the same amount in either case. So, there is no benefit to going short servo arm or long servo arm as it regards servo slop.
That leaves effective torque. A servo arm that is shorter than the control arm is more effective in moving the control surface and resisting blow back than the converse. Simple mechanical advantage.
I would also argue that the shorter servo arm is also more precise in that for any amount of stick movement, the servo connection point moves less, thus you can more precisely position the servo connection point with your stick. Granted, that doesn't change the amount that the control surface would move as compared to a equivalent longer servo arm/shorter control arm, but I'd rather put as much precision/granularity at the front end as possible.
Last edited by RBACONS; 03-24-2017 at 02:29 PM.