Yes, both osTicket and Jira Service Desk offer a Free Trial.
osTicket is designed for Individuals, Large Enterprises, Medium Business and Small Business.
Jira Service Desk is designed for Large Enterprises, Medium Business and Small Business.
Pricing for osTicket Starts at $9/User/Month whereas for Jira Service Desk Starts at $10One-Time Payment.
Some top alternatives to osTicket includes Zendesk Support, Zoho Desk, Tidio Helpdesk, Freshservice, Jira Service Desk, Freshdesk, HelpDesk, SysAid, UVdesk, Jitbit Helpdesk, eStreamDesk, ReadyDesk, Spiceworks Help Desk, HESK, BoldDesk and GLPI.
Some top alternatives to Jira Service Desk includes Freshservice, ManageEngine ServiceDesk Plus, SolarWinds Service Desk, Mint Service Desk, Symantec ServiceDesk, Freshdesk, HelpDesk, ReadyDesk, Milldesk, HESK, Scopedesk and GLPI.