It's no different from if you made an exact copy and then put a bullet through your own head. Your mind wouldn't jump to the other one. It'd be splattered all over the wall.
It is totally different! There is a lot less mess to clean up.
I think people get a little too superstitious about their sense of self... 'Your' mind, as in everything that makes your mind unique, would be copied over.
It's like if I had a CD, copied it over to form a second CD with the exact content, then smashed the first. Yes, I am breaking a CD, but nothing of value is lost, even if that CD had some very valuable data on it.
Indeed, everyone's fear of their consciousness being non-transferable is exactly that, our very human trait of assuming we are special and unique and a deeply-held fear of that not being true
Like everyone is now discussing, the real issue isn't with the nature of the differing consciousness, but with people's perception of the uniqueness of their individual consciousness and the belief that the reflected consciousness would not be identical to theirs simply because it is not the originator. If one might think of it as they would data on the internet... Sure, there is an originating file, but if a perfect copy is made and the file sent to twenty other individuals via internet, do they not all possess the same exact program that fulfills the same exact role, was created originally in the same exact location and time, and is perfectly identical in every way shape and form?
I wouldn't go so far as to fully classify the nature of that belief, you can research psychology for the answer to man's fears and beliefs regarding consciousness and spirit. What it really does come down to, though, is whether or not you TRULY believe there is a soul or not. I say truly because you can think you don't, yet your upbringing and culture may have ingrained within you that very same sense of individuality of consciousness even though you wouldn't attribute it to the accompanying spiritual terminology.
Me, I got over that fear a long time ago. I see the brain as a field generator, and our consciousness as a permeating energy and construct of our brain in its exact configuration. Our consciousness will metamorphose if our brain chemistry or shape changes due to blunt trauma, chemical interaction or extreme emotional stress, therefore I believe that our consciousness would, by my incomplete logic, not be TRANSFERRED by teleportation, but generated by the new brain on the other side. Not only that, but both the originator and the host brains would generate consciousness, though they'd not be the same simply due to the fact that they branched out in Time. The psychological stimuli created by transference would simulate meeting yourself from the past or from an alternate universe, if you want to put such a thing into perspective, since your consciousness changes every passing second. Any slight deviation in Time, neuro-chemistry, or stimuli would subsequently create a fork in the road and as such, your two identical consciousnesses would no longer be One.
Hello, tele-clone! A REFLECTION created via teleportation differs from a CLONE. A clone would be BASED off of an individual host's physical, emotional and mental reality yet the process of creating a clone, which must be aged, would invariably create a rift between the two. Now, teleportation...
Whether the entire body is being physically and energetically de-materialized then transferred through space in some sort of quantum particle state, OR the body is being reproduced as a perfect copy through a process more akin to that of 3D printing, the host would not be 'grown' as with clones, but reflected over to the receiving end of the bodily transference.
So, it falls down to three broad categories. In cloning, your genetic material is taken to create a mostly-identical copy of you who will develop its own branching consciousness, and two of the many theories of teleporation; the most common energy-transference idea where you are broken down to your base mechanical parts and fired through space only to be rebuilt on the opposite side via some sort of complex mechanical process, OR you'd be scanned to the very depths of your unique cellular makeup, your DNA structure entirely mapped, and a perfect replica of you created in whichever location contains the necessary equipment for such an endeavor.
Of course, if people believe its #2 yet its #3, we may one day end up with reflected 'clones' of us running around...
That'd be the day.