Read a little bit of the discussion thread. I used mysql to dump the wp_user table, displaying user_login and user_nicename fields. Rarely do they ever match. Many of the user_login values are for example 'John.Smith' and the user_nicename becomes 'john-smith'.
I don't know if case matters in your comparison, but anytime a user's user_login has uppercase characters, the user_nicename replaces it with lowercase characters.
Any blank character (space) is allowed in user_login but is replaced with a dash in the user_nicename.
Any period is allowed in the user_login but is replaced with a dash in the user_nicename.
I did not use a plugin that allowed me to modify the user_nicename. They are what the system created.