I imagine that much the same thing would have happened, only in inverse, so it would have been the Doctor who was killed and Sacha Dhawan would have regenerated into David Tennant :P

Well first of all the Doctor would have to be a fundamentally different person who is much curler and more immoral than they are now. Their morality comes from when they met Ian and Barbara and the talking to Barbara gave them in Edge of Destruction. So we must assume that the Doctor never met Ian and Barbara and never took on the Name the Doctor as a permanent title instead of a placeholder. This would mean the show itself is fundamentally different as well.

I the case the Master would never have taken on the name the Master and would have remained using the nickname of Kochie. They would probably be the protagonist due to their role as Truant officer (the reason they left in the first place before they got corrupted). It would also have political drama elements as well.

Of course the reason for the difference of character could go back further to the Rock Murder of Torvic in which Little Theta Sigma did become Death’s Champion.

In this show the Doctor (probably called something like the Warlord or the Barber Surgeon) would be the primary antagonist whilst Truant Officer Koschie would be he main character attempting to track down this Evil Renegade, eventually The Truant Officer would realise that their society is corrupt and realising this would set of into the universe to explore and run from their former bosses. They would take on a bunch of companies whilst the Destroyer of Worlds would attempt various plots to destroy them or to bring them to their side.

The plot you are suggesting would suggest and different show. A world in which Koschie grew up in to the Doctor and Theta Sigma grew up into the Master.

A very different but very interesting world.

@Anastasia Cousins However, considering that this Doctor is the one who casually murdered a bunch of Sontarans, Cybermen and Daleks without a second thought, it's less far fetched then you might think.

@Aquanafrahudy hummm. I still don’t think they would something as awful as completely striping the identity of the Master for no reason. The Master’s plot would be to Become the Doctor. Why would the Doctor want to become the Master? Unless they are a fundamentally different person,