TOS was on the air for three years. TNG was on for seven years. TNG was more successful during it's run. That is fact.
But it's not really comparable. TNG was first-run syndication, where the competition was considerably less than it would be in a network prime-time slot. TNG, like TOS, never cracked the top 30 in ratings, and it is highly doubtful it would have lasted as long as it did on one of the big four broadcast networks.
That's not entirely accurate, though. During TNG's real heydey, around the time of the 5th and 6th seasons, it was pulling in ratings that went head-to-head with its network competition. In particular, I remember Paramount being very proud of the fact that TNG was beating the ratings for Monday Night Football.
It may not be a direct apples-to-apples comparison, since TNG was syndicated, but people forget just how phenomenally popular TNG was. It definitely pulled ratings comparable to successful network shows, and I think it could have succeeded on a network.