Either option would work. I would recommend using a git pull to pull the updates to your master branch since this will also clean up any files that have been removed. Using FTP/SFTP would simply copy the new files over the old and would not handle deletions.

If you wanted to take things a step further you could add a script to your site that acts as a webhook. With this in place, merging your changes into the master branch on github could kick off a git pull on your server and keep your live site in sync with the master branch of your git repository.