Human hair: more versatility (can be heat styled and colored), longer durability and custom-styling. The most desirable form, Remy hair, has been cut from a human head of hair, as opposed to residual hair that has fallen or been brushed off.
Synthetic: easy to maintain (wash and wear), less expensive than human hair, easy to style, pre-styled to hold its shape. However, it has limitations not found in real hair that range from heating and styling to texture matching.
Choosing between a human hair wig and a synthetic hair is more of personal preference.
For example, a person looking for a wig they plan on wearing every day and that they can heat-style themselves would choose a human hair wig whereas a person looking for a wig that is easy to maintain and less expensive would choose a synthetic hair.