I'm not sure exactly why you're being downvoted, but I'll hazard a guess below.

I think yours is a pretty good question to be teased out, ya know? I believe you're asking "Wouldn't you just be making a robotic clone, and not an actual robotic self?"

So that's really a question of "what is self?" And I think it's possibly the source of your downvotes, because you're too close to asking about a "soul" on r/atheism for some. :-)

But under both of those scenarios that you outlined - robotic brain in human body, or robotic brain & body (possibly, more below) - you're still doing the copying one piece at a time, and if there's no loss of any data or data state whatsoever, and the destruction of the original is completed as well, then it's a perfect copy.

However, I can see your point, that it's still a copy - just like a file in a file system can be copied perfectly and still not have the same underlying file system data associated with the file, so too would the copied brain be such.

It's an interesting issue, because what if we could use the nanobots to upload our whole consciousness into a computer (again, with no data loss)? That second scenario you mentioned doesn't specify that the synthetic brain being built is in another body.

It also brings up a third issue which I think you forgot: what if the nanobots inspect the brain matter and the state of everything in it without destroying it - what if there was a machine that could do a scan of some sort to the brain and complete the same operation after the scan, with the nanobots just doing the replacement of the old cells? What then if they're not actually building the brain in the old body, but putting into a new body, or again, if the scan just goes directly into the computer. Have we just developed a perfect clone of your personality?

"If you guys are really us..."

Humor me... What if an alien ship floated above your house while you were asleep, employed such a scan on your brain, destroyed your house and everything in it after confirming your brain uploaded to their computer, and then they zoomed out into space and created you a new body, a new home, on some alien planet, tweaking your memory so that you thought you'd already lived there your whole life? Then you wake up from the wildest dream you've ever had, and go about your day on the alien planet.

Would you be aware of your other body's destruction? Would you still be you? Why would you have reason to care?

I guess it all really depends on what you define yourself as. What if the aliens came and beamed brain scans of everyone on the planet into their computer, destroyed this planet, and made us all wake up believing that we had all always had green skin color, matching the bodies they give us?

It certainly messes with your identity, but I freaking love the philosophical problems of science fiction like this.