I just wanted to bring up some numbers I posted in a comment on one of blog posts here.
Consider the last 12 seasons for both the NFL and NBA.
A random NFL team could expect an average of about 4.5 playoff appearances, while a random NBA team could expect an average of about 6.4 playoff appearances.
Actual NFL playoff appearances had a standard deviation of 2.53. Actual NBA playoff appearances had a standard deviation of 2.81
Looking at teams more than one standard deviation away from the average number of playoff appearances.
NFL teams with fewer than 2 playoff appearances: 4 (Buffalo, Cleveland, Detroit, Houston)
NFL teams with more than 7 playoff appearances: 3 (Indianapolis, New England, Philadelphia)
NBA teams with fewer than 4 playoff appearances: 3 (Charlotte, Golden State, LA Clippers)
NBA teams with more than 9 playoff appearances: 3 (Dallas, LA Lakers, San Antonio)
The numbers aren't entirely accurate because of expansion teams that were not active for that entire period (and I may have made transcription errors in spending the fifteen minutes necessary to run the numbers), but they should be about right.
Now, if you want to bring up competitive balance in terms of teams that actually win a title, one explanation is that the NFL has a single-elimination playoff system, while the NBA has multiple seven-game series. Luck becomes more of a factor. A few bad calls by the refs can knock you out of the playoffs in the NFL. A few bad calls may cost you the game in the NBA, but the better team can still overcome that and win the series. The NFL (by necessity, since there are only so many games a team can play) has a playoff system where the team that is the favorite is less likely to advance to the next round of playoffs (or to win the title in the final game/round).
To put it bluntly, if you think that NFL fans have more hope of winning a Super Bowl than NBA fans have of winning the Finals, the main reason is because it's a lot easier to get lucky in the NFL, not because of a hard cap creating more competitive balance. The defining feature of the truly hopeless teams tends to be bad management/ownership. No hard cap can prevent the Lions from being the Lions or the Clippers from being the Clippers.