This post is older than a year. Consider some information might not be accurate anymore.
FileZilla is capable of using ssh keys for using sftp. Sadly there is no native support and you need to convert the private key to PuTTY’s PPK format. Although FileZilla can do that for you. Go to Edit → Preferences and in section
SFTP add the private key file. FileZilla will convert that into the PPK format and your are ready to use sftp.