The Bulls are not as good as the Spurs, Thunder, Clippers, Blazers, and probably the Warriors.
The Mavericks are a team that I might pick over the Bulls in the Finals.
The Denver Nuggets are a team that matches up very well against the Bulls. They are arguably better along the wing positions and very arguably at the 4 position, as well. And have arguably as much, if not more, depth than the Bulls.
I think the Bulls are better than the Rockets, but that series would still be hard-fought.
The Bulls are more playoff-conditioned than the Cavs, but that is far from a guarantee that they will beat them. I fully expect the Bulls to have the best record in the Eastern Conference. They have a regular season coach, and a regular season roster (depth and quality players all over the roster). Cleveland is a year or two away from being pretty easy title favorites. But that time is not right now. Kyrie Irving is one of the ten (or so) best offensive players in the entire league. But he's an absolute liability defensively. Kevin Love is not good defensively, but I don't see why he can't just be put on Noah (who can't create much of offensive for himself anyway). And a front-line of Varejao/Thompson-Love-LeBron will likely make the Cavs as good, if not better, than the Bulls from a pure rebounding stand-point.
I fully expect Chicago to be a better than Cleveland to start the season. But the problem is that the Cavs will only get better as the season goes forward. The Bulls are more playoff tested, but a lot hinges on how good they can be offensively. And a lot of Chicago's offensive hopes rely on two rookie forwards (McDermott and Mirotic) who have never seen playoff action. Pau Gasol is the x-factor in a series versus Cleveland. If he is aggressive offensively (big 'IF'), the Cavs don't have much of an answer.
All in all, it is impossible to predict accurately who should be the Eastern favorite right now. Bulls would likely win a series right now, but 82 games in and Cleveland will only get better.
I can hardly imagine a case where Chicago or Cleveland beat whoever comes out of the West. This year might be the first year we see the Chicago Bulls get destroyed in an NBA Finals.