Initially, I thought you were taking a devil's advocate position. But, obviously, not.
Bettman was the BRAINCHILD behind the NBA's HARDCAP agreement in 1983!
Since you want to compare apples to apples, let's see what the difference between the "1984 to PRESENT DAY HARDCAP" NBA reality is vs. the '64 to '84 timeframe, shall we?
From '64 to '84 there were 9 different teams that won the NBA championship.
From '84 to present there have been 6.
The HARDCAP sure brought significant improvement, didn't it?
How 'bout them apples (to apples)?
In 1994 the NFL hardcap took effect. Since that time (the 1995 Superbowl) there have been 8 different teams win. (8/11 73% variance)
In December 1975 the "Rozelle Rule", for compensated (read 'penalized') free agency, was struck down. The NFL predicted that all the good players would go to warm climate teams, or big market venues.
From the 1977 Superbowl to 1984, there were 6 different teams that won.
(6/8 75% variance)
In 1968 John Mackey won a landmark free agency case against the NFL. (But, in 1977 the player's union effectively reinstated the pre-1968 status quo with the NFL through the Collective Bargaining Agreement!)
In the years of 1969 to 1976 there were 6 different teams that won.
(6/8 75% variance)
Prior to 1969 the Packers won both Super Bowls.
Tell me again how the percentages have been increased by hardcap salary restrictions!!!!
The NBA doesn't have a hard cap, their cap has exception rules is and is officially listed as a soft cap. Now one thing I do like about the NBA cap is they also have a minimum team salary and I think the NFL would benefit from that, most of the habitually bad teams in the NFL are also the cheap teams that don't spend up anywhere near the cap.
It took years for the Rozelle rule's abolishment to seriously effect the league, teams had key players tied up to long term contracts which delayed their entry into the new real free agency. By 84 free agency was in full effect and the predictions were by and large correct, the big market teams began to rule the roost. Not coincidentally that ushered in the time when the NFC, which mostly plays in larger media areas than the AFC and has higher team revenues, began their 13 year monopoly on the Superbowl with only 5 different teams hoisting the trophy, finally brought to an end by salary cap parity. Not only did these same 5 teams win over and over the tended to win in blow outs because they were the only teams that could afford to be that good. The NHL right now is in a period analogous to that 84-95 period in the NFL, the big market teams that can afford the most good players (with the exception of the Rangers who are just poorly run) have ruled the Cup and will continue to rule the Cup until some sort of competitive balance can be restored.
The facts are there and obvious to be seen by all, the era of the NFL when they had true free agency and no cap is the era of dynasties with a whopping 38% variation. So the cap has nearly doubled the level of variation and restored things to the same ball park things were in before the era of true free agency.