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The phrase "comparison of the two" is a perfectly valid and usable phrase in written English.
You can use it when describing two things to show that you are contrasting them or pointing out any similarities or differences between them. For example, "The comparison of the two candidates shows that Candidate A has a slightly higher approval rating."
Exact(60)
And yet a comparison of the two movements is instructive.
Write a biographical comparison of the two women.
The comparison of the two companies can be a bit unfair.
But without a direct comparison of the two vaccines, experts said, conclusions cannot really be drawn.
Maybe it was all of the comparison of the two women in the European media?
But what's more important is Glenn's comparison of the two filmmakers, to Desplechin's favor.
The dancing! — and a comparison of the two on that count yields something very odd.
Here is a head-to-head comparison of the two, as consultants might see them.
Write a brief comparison of the two maps, noting any changes in voting patterns.
In fact, few of us would be able to give a clear definition or comparison of the two.
Some of Verdi's borrowings from the opera he knew so well are revealed by close comparison of the two scores.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com