As EmCeeGramr pointed out you're Big Boss until the credits inform you that you were actually a distinctly different character, 'Phantom Big Boss', who died during the events of MG1.
They were never both Big Boss. There was the real Big Boss and his sub-boss Big Boss, you, the player.
They are separate people in the canon, and that steps over the metaphorical aspect in the mirror scene of 'there is no distinguishing between me and you, the player'. That's what I mean by a good concept mangled in execution.
Slightly confused by your last paragraph - 'steps over'? I loved that scene and I thought it worked.
By 'separate people in the canon' are you talking about Phantom Boss/Venom Snake being the Doctor from the GZ helicopter, who was an established person on Mother Base who happened to be in the chopper with Boss when it went down?
Imo that's answered in the tapes where they explain the 9 following years. Cipher spend 9 years hypnostising that Doctor character - indeed, a separate person - to have all of the Boss's experiences and memories (and probably his voice, too) - so that in the end, the pre-GZ Doctor character is basically non-existent. The whole world thinks he's dead, and his personality has been all but erased. For 9 years he is gone while Zero/Ocelot transform him into a second Boss. And if the definition of a person is just a human's thoughts and experiences - he might as well be the Boss. He has all his memories and thoughts and talents. (This is ridiculous, of course, but no more ridiculous than stuff which happens in MGS' 1-4.)
So basically pre-GZ Doctor has been turned into Big Boss, and literally is Big Boss (a second one who naturally isn't a flawless facsimile). What the player-as-character contrivance does is allows the pre-GZ Doctor to be
us. So that by playing The Phantom Pain we are physically enacting ourselves becoming Big Boss, and in the story it's justified so that we are given all of his memories/experiences.
I guess the execution was sort of convoluted, but I can't imagine how they could have done it much better. How would you improve it? (Without changing anything story-wise. Just as a fun exercise

))
I also just noticed that the whole 'being flawed facsimile of Big Boss' is basically our entire experience in MGS1, 2 and 4. Solid Snake is just as much a phantom of Big Boss as Phantom Boss/Venom Snake is. That's a nice parallel, in my opinion.
My view on her character is that nakedness wasn't the problem, the camera was. Nudity doesn't have to be sexual. (They don't allow sex on nude beaches, obviously.) If they'd played Quiet's scenes with the sense of respect that she gets from the other characters, the rain scene could have been one of the most interesting parts of the game, but they kind of donked it.
Very well said. Agreed on all counts.
It was verily donked.