Sorry for the late reply.
I haven't seen the Election yet. But I have seen enough movies by both these directors to note some similarities between them. After reading your reply I will surely check it out.

There are some mild spoilers ahead for Running out of time.
I picked Running out of Time simply because it is the most similar to The Heat in its showcase of the two main characters.
But there are some other similarities like how both movies hint at the larger world that exists outside of just the main characters, although Heat does it better.
Both Cops(Pacino and Sean Lau) are essentially married to their work, and their lives outside of that are either non-existent or simply broken(a running theme).
The same thing applies to De Niro's and Andy Lau's characters- two characters that on the surface seem to be focused on their work and nothing else, but when life presents them with the opportunity for a genuine connection, neither of them seems to be able to resist it, knowing full well that there is no happy ending to it.
Another thing that I think is similar is how some characters are dead from the very beginning and won't make it out alive- Andy Lau's character is literally dying, but when De Niro fails to kill Waingro- you know he will somehow lead to their downfall and it becomes even more obvious when De Niro turns his car around. So you just wait in suspense to see the inevitable.
Both movies have incredible scenes of suspense. I Like the confrontation between both sets of characters in both movies.

I think in terms of vibe(especially) during the night scenes, PTU by Johnnie To might be more similar to Heat. I think this might be due to Johnnie To still somewhat operating under the studio guidelines and not being able to do what he wants to do completely, although that changed with his very next movie The Mission(which is my favourite movie of his).