Not a teacher
"Favor" is more formal and correct. The usage also depends on the person to whom you are talking. [STRIKE]with[/STRIKE] If he's a stranger, then it's better to use the word "favor" [STRIKE]or[/STRIKE] but if he's close [STRIKE]one[/STRIKE] to you, [STRIKE]then[/STRIKE] you can use "request" too.
FaithHawks, please note the multiple corrections above. Your profile shows that you are a native English speaker. As such, you need to ensure that everything you write on the forum is correct because learners here will see your English-speaker status and will assume that they can trust your spelling, punctuation, grammar and spacing.
I have also added "Not a teacher" to your post.
In addition, I disagree with your suggestion that "favour" (BrE spelling) should be used with a stranger and "request" with a friend. A favour is a favour. If that's what you're asking the person to do, then that's the word that should be used, no matter who they are.