I think there is a Societal difference that plays into the topicality of TNG in comparison to TOS.
In the Sixties, so much was new and different to us.
Space Travel and an imagined wonderful techno future.
A generation grown from war into a belief in a growing and changing America.
Emerging racial and ethnic group awareness.
An Innocence we did not realize.
Experimentation with so much; drugs, social supports, philosophies, entertainment.
Freedoms and explorations of all shapes and kinds.
And in this, there was Star Trek reflecting so much of what was happening.
TNG caught us more hardened and with less dreams.
Apollo and true Exploration was on the back burner.
Shuttles were routinely flown, and rarely shown, except, of course, for...
Social ills seemed overwhelming and unsolvable.
Our failure were somehow more obvious than our successes.
Greed was Good.
The Needs of the One mattered more and more...selfishly.
Even our wars were fought differently...somehow not "honorable".
Subterfuge and flat out lying were more the order of the day.
Of course the differences were not as cut and dried as I might be making them sound, but they seemed so. We were more hopeful and innocent in TOS's time, IMHO, or, at least, more focused on the positive. And, indeed, had more positives happening, and more to hope for.
And that was the milieu, in both cases, that TOS and TNG were written in.
Topicality certainly exists for both, but I think examining the societal Venn diagram, if you will, is instructive and helpful in gauging that topicality.
Great Thread Topic, by the by, 'Frakes!