Large SQL Files
As of version 0.9.7, Sequel Pro can import and export SQL files which are multiple GBs in size without speed or memory issues.
When exporting SQL dumps, note the 'Use low-memory streaming mode' checkbox - this is unchecked by default, and downloads results as fast as possible to avoid locking up the server tables. If you are exporting very large tables, and the connection is not the bottleneck, ticking this will write results to file as they are retrieved to keep overall memory usage as low as possible. This does however result in the table potentially being locked for slightly longer.
mysql client and
If you have access to the MySQL Client on your host, it can sometimes be faster/more reliable to import sql files than via a GUI application.