Yes, both Jira and Teamwork offer a Free Trial.
Jira is designed for Large Enterprises, Medium Business and Small Business.
Teamwork is designed for Freelancers, Large Enterprises, Medium Business and Small Business.
The starting price of Jira begins at $6.25/User/Month when Billed Yearly, while pricing details for Teamwork are unavailable.
Some top alternatives to Jira includes Trello, Confluence, Asana, SwiftKanban, Kanbanize, ClickUp, Height, Kanban Tool, Kanban Zone and KanbanFlow.
Some top alternatives to Teamwork includes Quickbase , Smartsheet, ClickUp, Zoho Projects, Freshbooks, Wrike, TeamGantt, ProjectManager.com, Microsoft Project, ProWorkflow, nTask, Worksuite, Taskworld, Trackboard, Quick Base, Today, Resource Guru, Height and Project Insight.