I just watched that VOY episode and a few that follow it about a month ago.
Difference is that, aside from the actual episode he gets demoted in, nothing material happens as a result. It's just business as usual except they now call him "Ensign" instead of "Lieutenant. ". This was VOY's well-known weakness. Everything resets the following episode.
Not same the same about Burnham.
So, no, I can't agree with thus.
The only real difference for Burnham was that she wasn't bridge crew anymore.
Apart from that, she did the same thing as any other Starfleet officer as well, ever. She even had her own quarter and stuff, nobody was watching over her. The only difference was her rank. And since this was actually the first season - she wasn't even permanently transferred from her "usual" position. That was the position the "status quo" put her in. Saying her demotion "changed" her status quo is like saying Tom Paris "changed" his status quo when he got enlisted from his penal colony in the VOY pilot.
There was really no difference. Everything about Burnham reseted the following episode. The only real change happened at the end of the season, when she got "promoted" to bridge crew. Before that - was all the same status quo for the character. At least regarding her supposed "demotion" story.
I really see no significant difference in how DIS treated Burnham to how Paris was depicted on VOY. It's all window dressing, but beneath it is the same conservative approach to an intriguing idea.