Yes, both Jira and OneDesk offer a Free Trial.
Jira is designed for Large Enterprises, Medium Business and Small Business.
OneDesk is designed for Freelancers, Large Enterprises, Medium Business and Small Business.
Pricing for Jira Starts at $6.25/User/Month when Billed Yearly whereas for OneDesk Starts at $12/user/month when yearly.
Some top alternatives to Jira includes Trello, Confluence, Asana, SwiftKanban, Kanbanize, ClickUp, Height, Kanban Tool, Kanban Zone and KanbanFlow.
Some top alternatives to OneDesk includes Quickbase , Smartsheet, ClickUp, Zoho Projects, Freshbooks, Jira, Wrike, TeamGantt, Teamwork, ProjectManager.com, Backlog, Worksuite, Quick Base, Resource Guru, Jira Service Desk, HelpDesk, HESK, Height and Scopedesk.