Benzene behaves like an unsaturated compound because we can hydrogenate it albeit in harsh conditions.
C6H6+H2→C6H12
Benzene behaves like a saturated compound because you usually need harsher conditions for those reactions to occur. Saturated compounds are relatively less reactive.
For example, alkanes can decolourize bromine water however you need to meet certain conditions. An example of Cyclohexane:
C6H12+Br2→no reaction
C6H12+Br2→C6H11Br+HBr
Condition: UV
On the other hand, alkenes readily decolourize bromine water even in the dark. An example of Ethene:
C2H4+Br2→C2H4Br2
But Benzene needs a catalyst:
C6H6+Br2→C6H5Br+HBr
Catalyst: Anhydrous iron (III) bromide