Asik is currently committing 4.6 fouls per 36 minutes, so he's likely to have some problems with staying on the court. He's also shooting 38.6% from the line. If his defensive rating is 92, his offensive rating is 91.
Statistically, he's not as good at blocking shots as Jermaine O'Neal this season, so it would be reasonable to say Osik would provide much of what O'Neal gives with better rebounding, worse everything else, and an inability to reliably play much more minutes than JO due to likely foul trouble.
Pietrus/O'Neal for Hamilton/Asik might make more sense for Chicago than a deal involving Ray Allen. The Bulls would get a wing who is a better defender in preparation of a possible playoff series against the Heat.