Yes, both Asana and DeskTime offer a Free Trial.
Asana is designed for Large Enterprises, Medium Business and Small Business.
DeskTime is designed for Freelancers, Large Enterprises, Medium Business and Small Business.
Pricing for Asana Starts at $6.92/user/month when monthly whereas for DeskTime Starts at $87.08/Month when Billed Yearly.
Some top alternatives to Asana includes Quickbase , Smartsheet, ClickUp, Zoho Projects, Jira, Basecamp, Trello, Wrike, ProofHub, monday.com, Teamwork, ProjectManager.com, Microsoft Project, Quick Base and Height.
Some top alternatives to DeskTime includes clockodo, Time Doctor, TimeTracker App, Hubstaff, TrackingTime, Clockify, TimeTrack, Time Track Bill, Timesheet and Time Analytics.