Benefits & Drawbacks of Shredding
Since smaller particles have a greater surface area per unit volume, microbes are able to more easily get at more of the food. By chipping or shredding coarse materials such as twigs and stems, you will speed up the rate at which they will decompose.
Beware of Anaerobic Conditions
However, smaller particles will also decrease airflow into the compost pile. This may lead to anaerobic conditions, and the pile will likely need to be turned more often.