Well what’s the TIE convey? That he used a bad guy ship to fly out of his own bad guy persona’s gravesite? Or that it pairs with its good counterpart (the X-wing)?
Vader’s TIE says he is reclaiming something of Vader’s to put to good use, similarly to Anakin’s saber a little later.
The shuttle is just plausible, and has hyperdrive that a TIE like that wouldn’t. It makes sense for that setting. And in the shot it contrasts with the small X-wing like he had to hijack a bus or something to get there.
The insufferable nerd in me insists the shuttle is the better choice, as using Vader’s TIE trades one issue for another and grabs your attention to make you wonder how likely it would be for Vader’s TIE to even be there rather than whispering subtly about regular TIEs not being able to fly through hyperspace.