Chris Bosh, the number 3 free agent this year was the key complimentary piece to the big 2. The Chicago Bulls wanted him to help create a ridiculously talented roster that included LeBron James. Bosh really wanted to play with LeBron, but LeBron's loyalty to Cleveland doomed the pairing.
Bosh wanted nothing to do with Cleveland. LeBron and the Cavs wanted him which would have been a win-win for LeBron. Mistakenly, LeBron made Bosh too paranoid about getting left out that he went to Wade for the comfort of playing with one of the games top 3 players.
The Chicago Bulls, who already possess key role players in Joakim Noah and Derrick Rose, reacted quickly to losing the Bosh-sweepstakes by going to plan B. Plan B was Carlos Boozer who reportedly committed to a five year $80 million offer. http://sports.espn.go.com/chicago/nba/news/story?id=5361792
Personally, I think that the Bulls ended up with the player who fit their team better especially if LeBron is on it. Boozer is more of a low threat and averaged more rebounds than Bosh last year. He also put up almost the same number of points on a team with Deron Williams, a much better scorer than anyone on the Raptors last season.
Boozer is more of an inside player while Bosh has more range. With Rose and LeBron, the Bulls would have two outside options and be able to work better with a significant inside presence like Boozer.