Yes, both Zoho Desk and LiveAgent offer a Free Trial.
Zoho Desk is designed for Large Enterprises, Medium Business and Small Business.
LiveAgent is designed for Freelancers, Large Enterprises, Medium Business and Small Business.
Pricing for Zoho Desk Starts at $7/user/month when yearly whereas for LiveAgent Starts at $15/User/Month.
Some top alternatives to Zoho Desk includes Zendesk Support, Tidio Helpdesk, ManageEngine ServiceDesk Plus, Jira Service Desk, HelpDesk, SysAid, Desky, ReadyDesk, Sitehelpdesk, Trakdesk, HESK and BoldDesk.
Some top alternatives to LiveAgent includes Zendesk Support, Zoho Desk, Tidio Helpdesk, Freshservice, ManageEngine ServiceDesk Plus, Freshdesk, ClickDesk, HelpDesk, SysAid, Jitbit Helpdesk, Desky, Help Scout, LabiDesk, LiveChat, Zendesk Chat, LiveHelpNow and Little SaaS Communication.