Is your interest in nerve injury focused on research? Because if you're thinking about clinical applications, as of today, not much can be done for nerve repair except perhaps end to end suturing or nerve grafts (if anyone knows otherwise, please correct me). So as far as technical training to do this, any of the three specialties you mentioned are probably equal. You might also think about ENT as they frequently work with nerves in the head/neck region.
I would think that neuro would be most appropriate, especially if you're planning on doing basic science research in this area. But you're right, orthopedics does include work w/ peripheral nerves.
I assume you're fairly early in your med school career. I would say you should choose your area of specialty based on whether you like the bread and butter cases you'll have to do during your residency, and whether you like working with the diseases and patients you would see. Because ultimately you would be able to shape you research and clinical career to your interests no matter which specialty you choose.
As far as pros/cons, I think thats too difficult and too individual to answer - you have to do rotations in each and decide for yourself. Good luck.