This all depends on what is offered in the new position and on your negotiation skills.
Generally one tries to go up-hill, so to speak, or at least stay on the same level. The new institution hardly will expect you to make the transfer if they offer you a lower position and tenure track when you have tenure already.
If you are forced to move, then you have a weaker bargaining position and might have to take a tenure track position, and go through all the evaluation process again. But this would probably mean that you have bargained poorly or accepted bad working conditions, or it simply could be because there are so few academic jobs these days.
I have heard of one case where someone traded in a tenured Associate Professor position for an untenured Assistant Professor position at a better institute. (The risk paid off in the end.)