On the first RBT - entering from Burdon Rd, and taking 3rd exit onto Doxford Park Way - I would favour the inside lane because exits one and two appear to be too close for anyone to be cutting across from the outside lane to take either of these two exits.
Any vehicle entering the RBT from Mill Hill Rd, and behind you, would be taking the left hand lane almost immediately for exits one and two. If they were aiming for exit 3 (your exit, they would be moving across to the left lane somewhere behind you, to follow you into that exit. If you are in the r/h lane of the RBT, at some point you are likely to have vehicles on your left aiming for the same exit 3.
But we all know that many drivers hare around RBTS as fast as they possibly can (Oh, was a shame all RBTS are not compulsorily required to obey a 50kph - 30 mph - maximum as they are in France), and will weave between lanes to do just that. This is where total attentiveness and being prepared to evade the unexpected becomes essential.
Personally, I always circumnavigate RBTS at what I consider to be the appropriate speed, and am always ready to give way to any headstrong driver determined to rush through the RBT.