Pros:  Not having to implement the OS specific locking/unlocking of the session cache mutex in a multi-threaded environment.

Cons:  For the client the con isn't too bad unless the client would otherwise be doing a lot of session resumptions and/or there are device constraints making public key operations extremely slow on the device.  For the server, the cons are pretty big unless there are a low number of clients and they aren't doing session resumption.