I give Mandarin the majority.
By channeling his chi he can amp his strength enough to engage in hand to hand combat with Iron Man, and can even amp his martial arts strikes sufficiently to damage Iron Man's armor.
Add the 10 rings, and its Mandarin FTW.
Didnt need to write all that i know, but if this is the only post this gets, i wanted you to know my reasons.
Karnak strikes harder, yet BP beat him with just one hit, on two different occasions. BP is superior in h2h. The biggest challenge are the rings, that enchance Mandarins strength enough to damage IM, his durability and other things.
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As for the hth prowess, I believe it's safe to say Mandy is Karnak's superior.
Anyway, in this particular thread, Mandarin can do things like blowing up a building (which he is capable of), while BP will be struggling not only to survive, but to save civilians as well.
Off the top if my head, besides causing civilian casualties, the white light ring'd do the trick. Unless BP just Runs away and BFRs himself...
EDIT
Are you playing Devil's advocate, or do you think BP wins?
You said this'd be a great fight, but it has to have a winner, and no one's said it'd be a stomp.
I thought BP was given a massive upgrade recently though?
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I could of sworn part of his "upgrade" was good showings against someone more powerful then Mandarin. What has BP done with his upgrade then? Who was the powerful person he defeated?
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Got to give it to Mandarin. The environment just makes it easier for him.
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