What happens when I use a bigger capacitor?
The more torque you make the servos generate by moving or holding position the more current they require.  The faster this torque demand changes (particularly increases in required torque), the larger this capacitor needs to be.  The capacitor can provide power for very short-term demands, but mostly it reduces the change in current vs change in time for the power supply wiring.

If you have an oscilloscope, you can connect is across the capacitor leads and test your application.  If you see significant, short term dips in the power supply voltage you need a bigger capacitor.  If you see long-term dips in the power supply voltage you need to fix the power supply or power supply wiring.