The cPanel database backup option usually includes DROP TABLE and LOCK TABLES statements, whereas a default phpMyAdmin export does not, so this could explain the slightly increased size of the cPanel Database backup.
However, the large difference (half the size) in the "Quick" export to the "Custom" export seems a bit extreme, unless some of the format options have been changed. Has the "Quick" export outputted the data for instance?!
It's also possible that the cPanel and phpMyAdmin "Custom" options have outputted comments, whereas the "Quick" option may have omitted these. Although this alone wouldn't necessarily account for halving the file size, it could contribute to it.
In short, there are various options that can be set when exporting the database and these can all play a part in the resulting size of the database export.