Short answer is no. Don't get me wrong, I really like Heat (watched it again this weekend), but it isn't on the same level. Heat is a very good drama with interesting characters, but it lacks the underlying themes of the Godfather. The characters in Heat are laid out thoughout the movie and they never change. They do what you expect them to do:

Al Pacino sacrifices his marriage to pursue the bad guy, as he apparently has his entire career

Robert DeNiro sacrifices his relationship to get away (when he "feels the heat around the corner") just as he said he would

In the end, it is a very well done, well acted heist movie. No real deeper meaning to it. The Godfather on the other hand is a movie about a young man's desperate attempts to lead a normal life despite his family's criminal enterprises. Slowly though the movie, he is sucked into becoming his father, the leader of the "family", complete with all of the same vile and despicable traits. The acting is both films is great, along with the cast. I think the real difference is the depth of the story. It's like comparing Saving Private Ryan to Kelly's Heroes. Both great films, but one is a little more meaningful than the other.

I don't have an opinion. The word "opinion" implies the possibility I'm wrong.