Do due dates, priorities, and To-dos sync across devices?
This feature is in the plans though, and you can help to prioritize it by adding your vote to the feature request forums here:
iOS:
http://boxer.uservoice.com/forums/236855-feature-requests/suggestions/5484804-sync-due-dates-and-priorities-across-devices
Android:
http://support.getboxer.com/forums/256309-android-feedback/suggestions/6390071-sync-priorities-due-dates-and-assignees-across-d