FWIW, here is one Wisconsin perspective.
1) Bielema can recruit. He recruited high-character kids who wanted to play. In this, he actually did better than Alvarez, but he had a much better program to entice kids to. He always said he watched how a recruit treated his mother.
2) BIelema hired good assistants and treated them well.
3) Bielema was not a great game manager, but he ran a pretty efficient program. That alone could be mind-boggling for Illinois.
4) The biggest thing Badger fans have against BB is the way he left. Much of this, rightly or wrongly, has been attributed to his wife's influence, who, the story goes, was tired or running into women around Madison who gave her that "knowing look." They have been married several years now, with two young kids, I don't know that this will be an issue.
5) Badger fans will never forget Jen Bielema's "Karma" tweet.
I think BB will do well at Illinois, enough so that I would rather he took a job outside the B1G.