In the Premier League (as well as Formula 1, for example) there is positive feedback that keeps the top teams at the top. Being successful means that you make more money (whether directly through prize money, or indirectly through sponsors), and you can use that money to keep yourself on the top. Seven clubs have won the Premier League in the last 30 years (of which two have only won it once). If you support one of those top five or six clubs - good for you. If you don't, then you don't have a realistic chance of seeing a league win in your lifetime.
Whereas in the NFL the playing field is much more even. The player salary cap means that teams are limited in the ways that they can outspend each other, and there are various mechanisms that advantage the worst performing teams compared to the best (draft position and schedule). This means that with the right moves (usually the result of new leadership) your team can go from bottom of the pile to Superbowl contender in a short span of years. If you are a Jaguars fan and your team is picking #1 in the draft next week after getting one win last season, you can realistically hope that you might be supporting a good team in a couple of years. In the last TEN years, there have been EIGHT Superbowl winners despite what is considered to be an unprecedented period of dominance by the Patriots.
This makes the sport more interesting to watch as a fan - it's not the same few contenders year in year out. Even Formula 1 is moving in that direction for the good of the sport - bringing in spending limits and evening up some of the prize money distribution.