Here is how I see it (and this is with honest die hard bulls fan bias aside - I'm a realist).
Bulls are way deeper than Heat - I don't think even LeBron himself would refute that. Sure LBJ and Wade together far outmatch the combo of whomever you want to call our big 2 stars (Rose/Boozer, Rose/Deng, Rose/Scalabrine, Scalibrine in uni/Scalibrine in suit), but basketball is a team sport and that is the reason LeBron left Cleveland, his team sucked.
I look at it this way though. Wade/James only have each other to count on (maybe Bosh too, he's been left out a lot I feel like). The Bulls have Rose, and Deng, and Boozer (on the right nights) and Noah, and Korver, and Gibson.... ect. I'd play the zLaw of averages, you'd probably rather have 7-8 guys who consistently score 15 pts or more a game rather than 2 or 3 who get you 25-35 a game but everyone else is like 8-10. If either LeBron or Wade goes flat, even for a half, their entire offense suffers. If Rose goes flat for a half, there are 7 other guys who can keep the offense afloat. I'm not saying he can suck and we can still win - I'm just saying the short droughts will determine who can sneak ahead.
The Heat have 2-3 of the best defenders in the league but I think the Bulls TEAM defense is much MUCH stronger. A lot hard to score on a team who plays well as a group of 5 instead of 2-3 guys who are just good, all you have to do is get the ball to someone who isn't being guarded by one of them.
I dunno, I feel like its gonna be a BATTLE for sure, it can easily go either way IMO, I won't discount the Heat have a real good chance if they play it right. But even as a #1 seed, the Bulls thrive on being the underdogs and that's what it feels like they are here. Don't count them out by any means, they came to play, and play as a team, not 3 superstars who thought they could just walk in and own it.