Both options you can enable in Customizer - Appearance/Customize/Favorite&Compare settings tab.
Compare properties option:
Allow you to add 2 properties to the Compare Properties widget. You can set up which attributes should be compared. Clients shouldn't be logged in on your site.
Favorite properties option:
Clients can add 10 properties to Favorite Properties widget by clicking on hart from single property page of from overview. Clients shouldn't be logged in on your site.