From what i can tell by looking at both. It looks like the same exact book.
Bronstein, Zurich 1953 - editions?

If you're looking at the Amazon "search inside" versions, it is. If you click on "search inside for the Snowball edition, they actually show you the interior of the Dover edition. ("We are showing a sample of the Paperback edition (1979) because a sample of the Paperback edition (2013) from www.snowballpublishing.com you selected is not available.")
Or are you looking at actual copies?

I was looking at the links you provided. I have Bronsteins version and its one of the greatest chess books of all time.

Thanks. Is Bronstein’s edition a typo for the Dover edition? (I make that kind of goof all the time.). Or do you mean something else by it?

I have the "Snowball Publishing" edition. The contents are exactly as described by tlay80 in reference to the older Dover edition.

Dover edition = Bronstein Edition. That is, Dover is the publisher. Bronstein is the person who annotated the games. From the photo of the 'Snowball' edition it appears that it is simply a reprint of the Bronstein text. There also exists an edition of the Zurich 1953 tournament's games which are annotated by Najdorf.

And, of course, some say the opposite.
"Some say" is not a compelling endorsement.

I've heard that too, or at least more accurate in some lines. But I'm interested in the Bronstein because of its influence on successive generations, and because the annotations I've sampled look really interesting to me.

Bronstein came very close to winning the World Chess Championship against Botvinnik. The match ended in a tie, allowing Botvinnik to remain World Champion...
https://en.wikipedia.org/wiki/World_Chess_Championship_1951

Algebraic notation?
More or less. You can see it in post #7. The system used gives the square of origin as well as the square of destination.

The snowball edition is illustrated, i.e. it has photos of the players, just like Najdorf's book. The dover edition has no pictures and the font is just like in the typewriters of old. The dover edition is a translation of the corrected 2nd Russian edition. I'm not sure which version the snowball edition is based on.
What are the differences between these two editions of Bronstein's famous book on the 1953 Zurich Candidates' Tournament
https://www.amazon.com/Zurich-International-Chess-Tournament-Dover/dp/0486238008
https://www.amazon.com/Zurich-International-Chess-Tournament-1953/dp/1607966069
Is the later one to be preferred? Is it identical? I've never heard of the publisher, which is named as www.snowballpublishing.com. That website seems busted, which makes me wonder how legit they are. I worry -- is it a facsimile of some earlier edition with descriptive notation or something like that?
I can at least see a sample of the earlier Dover edition, which is in an ugly typewriter font and uses an annoyingly expanded version of algebraic notation (Bf1-c4), but I'd take it over a descriptive edition. I'm hoping, though, that someone well tell me the Snowball edition is actually better. Anyone have it?