Yes, both LiveAgent and Zendesk Support offer a Free Trial.
LiveAgent is designed for Freelancers, Large Enterprises, Medium Business and Small Business.
Zendesk Support is designed for Large Enterprises, Medium Business and Small Business.
Pricing for LiveAgent Starts at $15/User/Month whereas for Zendesk Support Starts at $19/user/month when yearly.
Some top alternatives to LiveAgent includes Zoho Desk, Zendesk Support, ManageEngine ServiceDesk Plus, Freshservice, Freshdesk, ClickDesk, HelpDesk, SysAid, Jitbit Helpdesk, Desky, Help Scout, LabiDesk, LiveChat, Zendesk Chat, LiveHelpNow and Little SaaS Communication.
Some top alternatives to Zendesk Support includes Zoho Desk, ManageEngine ServiceDesk Plus, Deskero, Support Hub, HelpDesk, Desky, Help Scout, Salesforce Service Cloud, ReadyDesk, Sitehelpdesk, HESK and BoldDesk.