I agree. This is one of the best scenes in American cinema, OF ALL TIME, period. HEAT is one of these rare, intelligent, emotional action films where you can't help but root for the bad guy AND the good guy.

But then again, there's really no good or bad guy here. Which is why HEAT is such a great movie.

That was a great scene but I heard that DeNiro and Pacino shot at different times and weren't in the scene together.

The new Righteous Kill actually has them as co-protags.

Guaranteed Al and Bob were behind the added dialogue.

Fantastic scene, and what's interesting is that he'd previously used it in a TV show called LA TAKEDOWN ... which has a very similar story to the film.

You can actually compare the two scenes ... I posted it in my blog some time back here's the link: http://writerjoshuajames.com/dailydojo/?p=868

It really shows the difference a great actor can make to a scene.

The reason either Mann or Pacino or DiNiro added the extra dialogue is because of this passage in the script:
'Both of these guys look at each other and recognize the
mutuality of their condition. Hanna's light laughter:'
It's telling the reader about an internal condition which, because of the later addition SHOWS what is said on the page.
A beautiful example of a basic requirement-Show it don't TELL it.
I can watch this movie 20 times a year and never tire of it.

the reason to add it is because not only have you got both deniro and pacino in your film, but you've got them sitting across the table from one another.. sure, give 'em more to say. please.

To attempt an answer to the question posed...
I'm sure there are other elements that would support reasoning behind adding dialogue not in the script (which, to an above comment notes the "showing, not telling" and I'd argue, it's still telling due to the fact it's dialogue, and wouldn't change even if the dialogue continued into VO and displaying the dreams)... but, I would venture to say that it is a comparison of character... Hanna is haunted by all the people he can't save and never will, because in his line of work, the victims are already dead by the time he comes into play. He has regrets about it but can't change it. Whereas Neil,despite everything, simply feels suffocated by the life he leads and SIMPLY needs a change to allow him to breathe.
Just my two cents.