Large File Transfers | FTP Alternative

I've started doing freelance that work that often involves working with very large files that don't compress well (e.g. video). I need a method that allows me to transfer these files to other in a fast and secure way. I'd prefer free, but since this is work related if there are some not too expensive options, I'd consider that too. Thanks for the advice.

Also, I don't like Dropbox type services or FTP because I find it too slow. Any FTP alternatives or replacements ideas would be great~