“So nobody complain if lubavitchers call their Rebbe the nasi hador. That’s our title.”
As I have written in the past in response to our erstwhile poster chabadshluchah there is a difference. The concept of gadol hador is well-known and has always been well-accepted. The concept of nasi has not been in existence for many many centuries, and has no meaning. It was adopted by lubavich – possibly because no one else uses it – to indicate that their rebbe is the undisputed and unparalelled leader of the generation. Something that many of us totally disagree with.
Also, what do you mean by “when he is not alive physically”. Why can’t you just say “not alive”? That always means physically by Yidden.