First and foremost, there's too much to quote in here so I'm just gonna reply like this. First, to whoever said the Bulls can't stop DWade...he had his worst round in the playoffs against the Bulls. Beyond that, the bulls shut him down to a tune of 9/37 FGs, for an average of 12.33 ppg during the regular season. I'd say, if any team in the NBA can shut him down, it's the Bulls.
Secondly, Shaq is showing his age. He didn't dominate at all during the playoffs with the exclusion of the deciding game against the Bulls. I think he's going to continue to decline and be less of a threat this year once again. You also have to wonder if he can stay healthy, which is going to be a question mark for him for the rest of his career.
Next, the Bulls won't have the best offensive starting five, but not only should they have the best defensive team in general next year, but they'll also have probably the best bench in basketball. This team is even deeper than what they were last year, so while they won't get a lot from the starting five because of Ben Wallace, the team is going to get a ton from their bench, with people like Nocioni coming off.
On the note of the bench, this has a huge advanatage over most teams in the NBA because of their ability to 10, 11, maybe even 12 deep. They don't have to play their starters in extended minutes, keeping them fresh for a lot longer than those teams with starting fives logging 40minutes or so per game.
Now, as to why I think they'll be better than the Nets, but maybe not the Heat. First and foremost is balance. They'll probably have at least 4 players averaging in double figures next year (Gordon, Deng, Noc, Hinrich), maybe even more depending on how much JR Smith plays and how well PJ Brown plays. Plus, you throw in Chris Duhon, and while he may not be the best scorer, he can still score.
Next is the depth of the team. The Nets bench isn't all that deep...while the Bulls aren't afraid to go 10 or 11 deep. Outside of their starting five, they have Duhon, Noc, Mallik Allen, Smith, Tyrus, Sweetney, and maybe even Songaila if he returns. That's some insane depth right there, and that's always good to have, that way you don't have to wear your starters down throughout the year.
Plus, last season, the Bulls won 2 out of 3 last year, with the only loss coming by one point and at the beginning of the season when the Bulls weren't playing well. This year, the Bulls are even better, while the biggest acqusition for the Nets so far has been Marcus Williams.
All in all, the Bulls are deeper, better defensively, and have plenty of offensive firepower, so in my opinion, there's no reason as to why they can't be better than the Nets.