Like I said before the what-turned-out-to-be-perfunctory Game 5, one narrative benefit to the Heat winning the title is that they're just another great team now. The Bulls or anyone else don't have to beat them to save basketball and prove anything beyond being the better team.
But while their accomplishment makes them easier to stomach, one potential drawback that Doug Thonus points out is that whatever pressure lifted now may make the Heat even better next year. It definitely means there won't be any major changes, though figuring there would be after a potential 2nd round exit (remember those days?) would've been for the sake of change and likely just make Miami worse. But now their top 3 players are certainly staying, and Eric Spoelstra has some job security. They have another offseason to make signings of ring-chasers, and may actually do well this time (though Battier and Miller certainly stepped up in the Finals, and little else matters I suppose). Even their luxury tax bill could be alleviated a bit if Mike Miller retires and they amnesty his deal.
But while Doug says this may mean it could be best to just pack it in until 2014/15 (move Deng for a pick, wait for Mirotic, there's more at the link...), I hope that's not the case. Though I do see that side of it, it's a gamble either way compared to staying the course and waiting for Rose with much of this team together. Now if you're being cynical (and I will be!), if there are comparable options, the Bulls will likely just go with the cheaper, more 'hopeful' one. Doesn't mean it can't work out, but I'm not a fan of that decision-making process.
Should we be more scared of Miami now and plan accordingly? I think that if both teams were fully healthy, the Heat would be favorites but it was close. A team next year with a likely lessened Derrick Rose, some key depth missing, and Carlos Boozer existing, makes it probably less close. But you would be there to strike if one of Miami's key players went down, like the Pacers and Celtics almost did.