I am having small doubt to make exception handing in flowable whether it will implement via System task or script task, there is no any specific activity task given either in eclipse designer or UI based modeler for exception handling.
I did not understand your question. Could you elaborate it more please?
If you need examples related to bpmn error handling, have a look on
org.flowable.engine.test.bpmn.event.error.ErrorEventSubProcessTest
in flowable source