TOS's final season had a viewership on network TV lower than STNG in syndication! This was at a time when TOS was basically on one of only 3 channels available, and no VCRs or video games, etc.
You can't directly compare TOS and TNG ratings. Yes, TNG was seen by more households/viewers but the number of households in the US had almost doubled since TOS time. TOS had better ratings but as you say it aired in the 3 network era. So comparing their ratings is never going to be apples to apples.
But there is no doubt that TNG achieved more success as evidenced by its 7 year run that could have been much longer if not for the movie series and creation of UPN.
For the only year I have ratings for TOS, BOTH the rating AND households are well below STNG.
RAMA