When you create a Task list in SharePoint you can see two options in List Settings tab depending how the Farm has been configured.
Two options are
- Connect to Outlook
- Sync to Outlook
Users will see Sync to Outlook option if a Farm level feature called “Farm Level Exchange Tasks Sync” is enabled else they will see Connect to Outlook.
Note this feature is accessible only from Central Admin under Manage Farm Features.
Issue with Sync To Outllok option is that just enabling this will not make Sync To Outlook work properly, most probably you will get error like below
We weren’t able to start syncing your tasks because one or more prerequisites for connection to Exchange server could not be found. Please contact your Administrator to resolve the issue.
To make this lot of prerequisites are required, details can be found here
If this works it means that Tasks will be synced at real time on all devices on which you have Outlook and you can Sync only the tasks Assigned to you. Unfortunately if the prerequisites are not met users can get frustrated by above error message.
In case your organization cannot fulfill prerequisites for Sync to Outlook then best is to go for Connect to Outlook which can at least make a Copy of Task list but not on all devices, only on current device.