Reference-
http://www.imixs.org/doc/core/index.html
I am having a requirement of creating tickets and manage its status one after the other depending on work flow process and i need to give roles to the users and give authority of who should edit data and who shouldn't
so which of the 2 above is better(easy) to integrate to a java application already existing to get work flow process to the java application
Activiti and Imixs-Workflow follow different approaches. Where Activiti is a BPM plattform focusing on process automation, Imixs-Workflow is a workflow engine focusing on human-centric workflows. Human-centric workflow mean to track a business process form the users perspective (e.g. provide a task list, send e-mail notifications or control the access and ownership of a process instance). Assigning roles and user rights to a process instance is one of the core concepts of Imixs-Workflow. So from your requirement description Imixs-Workflow is possible more aligned to your requirement.
Both engines support BPMN. So you can model your process with the BPMN 2.0 standard. Imixs-Workflow uses the BPMN 2.0 extension mechanism to encapsulate the technical details inside a process. Activiti processes a BPMN 2.0 model directly and uses the technical aspects and BPMN 2.0.
Activiti integrates with Spring where Imixs-Workflow is based on Java EE. So there is also a architectural aspect you should consider.