What do you mean by “mechanical gyros”? Spinning flywheels or MEMS?
http://en.wikipedia.org/wiki/Vibrating_structure_gyroscope
Fiber Optic Gyroscopes are laser gyroscopes. They are more accurate than mechanical or ultrasonic / MEMS gyros. The problem with FOGs is that they require a spool with many hundreds of metres of optic fibre as a laser light path and a digital processor. That makes them bulky and require a significant power supply. To stabilise a targeting system would require at least two FOG modules. FOGs are suitable for navigation because they can sense the rotation of the Earth and so find the True North meridian. They make an accurate compass, something that MEMS cannot do.
3D MEMS gyroscopes are now the obvious choice for fast servo stabilisation of handheld or tripod mounted platforms or equipment. They are light weight, robust, low power and have a fast response.