I went to Penn State, which used to be independent and found itself squeezed out of championships and the like because of the political influence of the conferences. It became tougher and tougher for Penn State to be able to put together a schedule because of conference conflicts and rules.
Also, Penn States other athletic programs, like Basketball and Baseball, which didn't garner much interest, became stronger as a result of having to compete as part of the Big 10.
Penn State's football program has not been hurt, and in some instances helped by it's association with the Big 10. They don't appear to win quite as much, but it's hard to say why as every season there were always other programs that were putting out excellent football teams, even when they weren't part of the conference, and they never ducked a good team while trying to get the national title.
The main benefit for Penn State, is that when they are good enough to compete for a title, the entire Big 10 is behind them, and their political clout ensures that they get consideration.
I think that other programs are running into the same problem, or are in conferences that are too small or weak for the school. The Big 10 has 11 teams, now it will have to be renamed if Nebraska joins. I also wonder what will happen to Notre Dame, they too run an independent program, and used to have a fan base that enabled them to get away with it. Not anymore, that program is dying and needs to be a part of a bigger group to keep it going through the lean years.