I'm not a fan, but I think he doesn't really get his due from the Badger fans--mostly because we were mad at him for wanting to go somewhere else.
Alvarez was 118-73-4 at Wisconsin during his 16 years as the head coach. That's a win percentage of .605. Take out his first three seasons (so starting with the '93 Rose Bowl team), and he was 106-52-4, or .654. He had three conference championships, two one-loss regular seasons, and went 8-3 in bowl games, including going 3-0 in the Rose Bowl. After '93 Alvarez had two more losing seasons ('95 and '01). His '93, '98, and '99 teams were among the best in Wisconsin history.
Bielema was 68-24 at Wisconsin, or .739, in seven seasons as the Wisconsin head coach. He had two conference titles, two one-loss regular seasons, but went 2-4 in bowl games (Alvarez coached the Rose Bowl in the last/seventh season--a loss that I don't include above because he wasn't the head coach). His worst season was the 7-6 '08 campaign. The 2010 and 2011 teams were among the best in Wisconsin history (and played better teams in the Rose Bowl than the '93 and '99 squads).
Arguably he was more than just a caretaker. The Badgers were more consistently at the top of the Big 10 under him. And even if he didn't improve the team, he maintained (with a substantially higher winning percentage) the program at the best level it had ever reached.