Error log flooding with aborted connections (Aurora 2.03 - MySQL 5.7.12)
The aborted connections log messages are controlled by the log_warnings setting. In MySQL 5.6 it is set to 1 by default whereas in 5.7 the default is 2 (which is more verbose and shows connection messages)

You can compare the description of the settings for 5.6 vs 5.7

https://dev.mysql.com/doc/refman/5.6/en/server-options.html#option_mysqld_log-warnings

https://dev.mysql.com/doc/refman/5.7/en/server-options.html#option_mysqld_log-warnings


  Print out warnings such as Aborted connection... to the error log. This option is enabled (1) by default. To disable it, use --log-warnings=0. Specifying the option without a level value increments the current value by 1. Enabling this option by setting it greater than 0 is recommended, for example, if you use replication (you get more information about what is happening, such as messages about network failures and reconnections). If the value is greater than 1, aborted connections are written to the error log, and access-denied errors for new connection attempts are written. See Section B.5.2.11, “Communication Errors and Aborted Connections”. 


As long as the defaults weren't changed I wouldn't expect to see the connection errors on the 5.6 server. You could try setting it to 2 and checking the log again: set global log_warnings=2;