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Both are technologies to drive Message Driven Beans. The key difference is that Activation Specifications are the JavaEE standard way of defining them. Listener Ports was the mechanism that WebSphere Application Server used prior to the adoption of Activation Specifications.Listener Ports therefore were stabilised in WAS v7; any new MDBs should use Activation Specifications. Liberty for example has no concept of listener ports.
More information in the Knowledge Centre http://www.ibm.com/support/knowledgecenter/en/was_beta/com.ibm.websphere.base.doc/ae/cmb_ovrvw.html