Wordpress 4.2 introduced support for "utf8mb4" character encoding for security reasons, but only MySQL 5.5.3 and greater support it. The way the installer (and updater) handles this is that it checks your MySQL version and your database will be upgraded to utfmb4 only if it's supported.
This sounds great in theory but the problem (as you've discovered) is when you are migrating databases from a MySQL server that supports utf8mb4 to one that doesn't. While the other way around should work, it's basically a one-way operation.
As pointed out by Evster you might have success using PHPMYAdmin's "Export" feature. Use "Export Method: Custom" and for the "Database system or older MySQL server to maximize output compatibility with:" dropdown select "MYSQL 40".
For a command line export using mysqldump. Have a look at the flag:
$ mysqldump --compatible=mysql4
Note: If there are any 4-byte characters in the database they will be corrupted.
Lastly, for anyone using the popular WP Migrate DB PRO plugin, a user in this Wordpress.org thread reports that the migration is always handled properly but I wasn't able to find anything official.
The WP Migrate DB plugin translates the database from one collation to the other when it moves 4.2 sites between hosts with pre- or post-5.5.3 MySQL
At this time, there doesn't appear to be a way to opt out of the database update. So if you are using a workflow where you are migrating a site from a server or localhost with MySQL > 5.5.3 to one that uses an older MySQL version you might be out of luck.