I think that for initial instruction, it is beneficial to be able to demonstrate skills the same way the student will be doing them. There are very few cases where that makes any difference, but there are some. The most obvious is alternate air. If you are demonstrating using an Air II type of system and the student has a conventional octo, your demonstration will not do much good. The same is true for weight belt/integrated weights and removing replacing the scuba unit under water. Other than that, I don't think it matters.
Once you have gotten past the pool, variety can be helpful by extending the student's horizons and knowledge. When I do OW dives, I am no longer demonstrating. I use a back plate and wing with a long hose and bungeed alternate. I recently did the OW dives for a single student for whom I was not the pool instructor. When it came time for the alternate air exercise, he used his conventional octo as he had been taught to donate to me, and I used my long hose to donate to him. No problem, and his knowledge was extended.
Once you have gotten past the pool, variety can be helpful by extending the student's horizons and knowledge. When I do OW dives, I am no longer demonstrating. I use a back plate and wing with a long hose and bungeed alternate. I recently did the OW dives for a single student for whom I was not the pool instructor. When it came time for the alternate air exercise, he used his conventional octo as he had been taught to donate to me, and I used my long hose to donate to him. No problem, and his knowledge was extended.