The privilege at issue is the same as the one that was in the U.K., which is the control over the proceedings of Parliament. It is the ability of the House to make determinations about how it's going to operate and how its procedures and usages will evolve with time.
In this respect, the privilege is the same one. It's the exercise of it, how it's being exercised, how different assemblies are choosing to adopt different procedures. That doesn't have to be the same, but what is the same is the autonomy for those decisions that will be respected by the courts.