the definition between a rotation from one orientation into the other assumes an identical coordinate system, i.e. cubic-cubic. If you describe an orientation between two different coordinate system you have to take into account that the orientations refers to an orthonormal coordinate system. This is often not extremely critical if you are discussing orthogonal systems, but even there it depends how do you describe a crystal coordinate system by an orthonormal basis, i.e. e1 || a, or b or c. Only for cubic it makes no difference since you can define a,b,c as you like. Taking this into account the answer is: it depends how do you define your crystal coordinate system with respect of the orthonormal axes. A bit about these problems you can read in the linked papers. It is related to Euler angles but finally all works using an orientation or misorientation matrix and from this matrix you can derive very easily the angle and axis. how this works you can see in the presentation (second link). There are many books and publications which are focused on this topic, but nevertheless many people are puzzled by all these conventions used. Good luck! And please keep into account that the next paper already defines everything in a different way...
Thank you for your valuable comments. The Angel-Axis values for the Shoji-Nishiyama (S-N) orientation relationship between epsilon-martensite and austenite have been calculated as follows;