Short answer: both.
As gracer says, when we speak, we move our lips, tongue, face, and jaw - not to mention our glottis, vocal folds, and diaphragm - in very finely tuned synchronization. All of these things go into producing our particular accent. Beginning the moment we are born, we begin to distinguish the catalog of sounds that will make up our accent, and we teach our muscles to perform the movements that produce these sounds. And we learn to make these movements, some of which are incredibly small, in relation to the architecture of our own mouths and throats. This process can take many years, and sometimes, it’s never completely successful: think about all the kids who still have trouble pronouncing “r”, “l”, or “th” at 7 or 8 years old, and all the adults who never do learn to roll their "r"s (or refrain from rolling them), or who speak with a lisp.
In this scenario, then, let’s say the transplanted consciousness (Mr. T) wants to produce an “r”. This desire triggers various nerve impulses in the brain that translate into something like, “produce energy to contract styloglossus X millimeters, contract obicularis oris Y millimeters at 90 degrees and 270 degrees”, and so on. (And as Lasciel points out, this is presuming that the new brain is capable of producing identical impulses to the old one, which is indeed highly unlikely.) The muscles will then try to perform these movements. But they will not be developed to the same degree as those in Mr. T’s original body, so some will contract less, or more, and some may not move at all. Further, even if all the muscles did move exactly as they did in Mr. T’s original body, his new mouth is a different size and shape. So a contraction of those muscles should have made the sides of his tongue press against his teeth at a certain position with a certain amount of force, but now, the position is different, or the force is greater, or perhaps the tongue fails to meet the teeth at all. The result might be a completely different sound entirely - a “d”, or an “s”, or a “u”.
So I imagine that the “accent” that comes out would be neither the accent of the original owner of the body, nor that of Mr. T. Instead, it will be a very muddled version of Mr. T’s, as though he’s trying to do ventriloquism with a mouthful of Novocaine and a brand-new retainer. And it will be many years before he learns to produce his original accent again, if ever.