Delegation is better than inheiritance when the object doesn't want to export the full interface of the parent class. It is also useful when the object wants to change the behavior so much that it isn't a direct replacement. Also, it is helpful when the relationship needs to be dynamic, if the "parent" class is dynamic, or the referenced object needs change dynamically.
For example, many network client classes inheirit from IO::Socket::INET. This is convienent for both internal and external use. But it fixes the clients to only use IPv4 sockets. There are other types of sockets, like IO::Socket::INET6 and IO::Socket::SSL, that could be used if the inheiritance wasn't fixed.
Also, there is a need to change the socket but keep the same client object. Some protocols support negiotiating SSL over the existing TCP connection. The easiest way to support this is replace the reference to the IP socket with an SSL socket object.