why is it in smaller airplanes with mechanical Attitude Director Indicators, for example in light single and twin prop planes that the Roll pointer goes in the direction of the turn, while on Electronic Attitude Director Indicators, the pointer goes to the opposite side?
The difference is not "small plane" vs. "large plane." The difference is mechanical vs. electronic display capabilities.
In a mechanical ADI, the Angle-of-Bank [AOB] pointer is oriented (fixed) relative to the display's glass panel (i.e. the cockpit). IOW, the pointer always points to the top of the cockpit/plane and the horizon moves behind it.
The physical limitation of the mechanical ADI is that nothing can be placed on the horizon "gyro" since it will move out of sight with any up/down pitch.
An electronic display has no moving parts, therefore no physical limitation on how information is displayed. These are just computer generated images and how you program the computer controls how information is displayed. IOW, an AOB oriented to the real world horizon will be in view at all times.
So why the change you ask? With physical limitations removed, instrument designers are free to apply more human-factors engineering to how an instrument displays information. IOW, what's the best way to display information so the pilot sees and knows
what he is seeing almost instinctively.
In electronic ADI's the AOB pointer is always pointing toward the real world "up" [pilots already know where the top of their cockpit is]. For most normal flight operations that makes little difference [heck, most planes I fly have both and I never noticed the difference until this question was asked and I did a little research]. However; during extreme unusual attitudes where the horizon line may be out of view, the pilot is seeking exactly
that information... where is UP
in the real world. Therefore, the better human-factors display is one where the ADI shows the pilot where real-world "up" is at all times and that is the display where AOB is fixed to the horizon [moves with the horizon] which is only possible with electronic instumentation.
Instrument designers have gone one step further by programing the electronic ADI to enlarge/enhance the AOB pointer into what is known as a "sky pointer." Usually large, sometimes flashing arrows pointing "up." AA
's HUD adds even more symbology all showing where the horizon is (or "where is up").
Hope this helps.