If you just move the same old matter from A to B albeit in a somewhat exotic form
This is the theory (maybe in different details) that I think is closest to what's happening.
The transporter take you, a physical person, changes you into a "energy person," who is still a living being.
Then it sends you (holding you in that state) to the destination.
Then it either changes you back to a physical person, or basically just lets you go, at which time you naturally/automatically revert back into physical person. (per That Which Survives, and Second Chances)
The process is quite fast, but during the process you are aware of your surroundings. (per Barkley's experience. and Kirk and Saavik conversation in TWoK)