As of now (SQLyog 5.12) both the SCHEMA SYNC tool and the DATA SYNC tool operate in a case-insensitive way, as far as table names (but not string data, of course!) is concerned.
There are plans for the near future to query the system variable 'lower_case_table_names' and perform the sync case-sensitive or case-insensitive according to the values for 'lower_case_table_names' retrieved.
Note that if not explicitly set the 'lower_case_table_names' system variable takes it value from the system variable 'lower_case_file_system'. That is why Linux most often is case sensitive with table names and Windows most often is case-insensitive, for instance.
Also note that columns names always are case-insensitive with MySQL.