I read The Glass Key knowing that Miller's Crossing was based on it (so it's hardly a secret) and afterwards I still had to see the 1942 movie to understand how one could become the other.
The 1942 version (Alan Ladd and Veronica Lake, for those of you without a horse in this race) isn't all that great. The one thing I really enjoyed about it was the raw physicality of Ned in the fight scene. I'm always surprised when black-and-white actors take off their neckties and physical in a really expressive way.
The situation is the same, definitely. The plots are different. The Glass Key is a mystery. When the murder is solved, the story's over. In Miller's Crossing, a murder sets the plot in motion, but it's essentially trivia. Tom eventually finds out whodunnit and why, in a couple of casual conversations, but nobody cares. That's not what the story is about.
I wrote a very long essay about the two at one point, essentially to prove that the trajectory of both film and novel is the lead's changes in station mirroring his changes in emotional life. Which is to say, at the end of The Glass Key, boy and girl rip up their previous lives and skip town together, frightened and heartsick and determined to be acontextual; in Miller's Crossing, boy and girl could have done the same, and don't. I always thought that Hammett's story was the one that made me wonder what happened after; the Coens' version is quite a bit more cynical, and final.
When you look strictly at "what plot events drive the action?" then they are very different films. (For one thing, they take place in different cities. And for all Hammett was writing contemporaneous fiction and the Coens are creating a period, the film has so much more real-world context.) But when you look at the emotional throughline of the lead and his best friend, they are identical. When you look at specific scenes and events, they have a very large number of striking similarities. Even the death-symbolism of the titles: the glass key to the door that keeps out the snakes shatters in Ned's hand, and the snakes come in and eat them up; the hat swirls through the titular execution ground, and Tom has too much dignity to chase it.
(I use "plagiarism" in this case with some affection, because Miller's Crossing is quite a good movie, but, I think it's an even better movie when you know its source materials. I for one was never informed of the literary antecedents of the film, and I think the filmmakers would come across better if they openly stated their intent to homage.)