What's the easiest and fastest way to transfer FTP files from one server to another?

I have ~ 40k files and uploading them with FileZilla can take a while. 

Does anyone know a better way?

You can use Rsync

You can use Rsync

​How would I use that?

You can find a lot of info at Google on how to use it like:

http://www.tecmint.com/rsync-local-remote-file-synchronization-commands/

but you will get a ton of tutorials if you search for Rsync remote usage

Just zip all the files before transferring them, then unzip them on the remote server.