My preference is wood. Traditional, functional, and attractive. Stacked leather and stag have also been used for hundreds of years as hunting knife handles.
Synthetics might be more functional, offering a higher level of durability and perhaps a better grip (thinking canvas micarta specifically). But the loss of aesthetics, military-wannabe connotations, and departure from hunting traditions are trade-offs.
In short, there's no 'right' or 'wrong' answer. Almost any material commonly used for knife making will be suitable for hunting tasks.
-Bob