A T* version of any lens is indeed newer than the non-T* version, except for the Sonnar-Superachromats and UV-Sonnar.
Having a single layer coating or T* multilayer coating is not that much of a difference: both coatings are pretty good. And using a lens shade will do much, much more to improve contrast than going from one layer to multilayer coating anyway.
But since non-T* lenses are older than their T* counterparts, there are those things to consider that come with age.
Which brings us to the "much newer" part of the question.
The first, single coated, 150 mm Sonnars were produced in 1956. They were given T* multicoating in 1975. Quite some time later. (By the way, the lens was first produced with black barrel in 1973 already. So when people tell you that the "chrome" ones are single coated, the black ones have T* multicoating, you'll know better. ;-))
The "C" version of this lens was discontinued in 1982, when the CF version appeared. Which in turn was replaced by the current CFi version in 1999.
All of them are good, all the same design (only micro-adjustments to the original design were made in these thransitions from one barrel-version to the next).
I'd say that, unless complete trashed, a later version will always be a better but than an earlier version. Simply because these things, like anything, do wear with age.
But even a first version "chrome" C lens would be a good lens to have. Provided it is in good shape.