uspsjuan
Gears of better material. The only deviation would be the engine. A modern engine would give it the power and reliability it deserves
Not necessarily.
The gearing in late-war Panzers was suspect mostly for not being designed to the task very well. Usually dues to trying to make too few HP move too much metal faster than intertia might allow.
Modern tank engines are "better" (and that's a very relative term) largely for the quality of their accessory bits. And, largely, for being able to be yaned out as entire units for repair/rebuild on a stand, rather than in the confines of a crowded engine bay.
Now, modern engines are going to be 'better' for not being ad hoc things like multi-bank, or paired combos and the like.
The King Tiger does not have that generous an engine bay, there's no way to shoehorn a modern power pack (or even a period soviet D12) in there.
Also, as a thught exercise, it's easy to dismiss the weight of a "full tilt" replica. That is unless you have some experience moving 40 or 50 ton vehicles around, and the permits wanted to trailer them.
A twenty ton "thin skin" replica will be either 16 time or 64 times easier to move around than a "full on" 60 tonne replica. And, if a person had either, they would be asked to share their toy and not just piddle about within their own 30-40 acre sand lot.