Testing on SQL Server 2008 shows that these queries not only give the same results, but even have the same query plans. The query optimizer already knows that these queries are equivalent. Therefore, you are correct that any argument that promotes one another will have to focus on other aspects, such as style.
For me personally, the second query is easier to understand, although the first query follows in more detail how you will express your search in English, because I saw EXISTS much more than ANY . The first request makes me go “wait, what? Oh yes, that's right ...” The second is immediately obvious to me. This may be different for others (perhaps for you); you should try to make sure that your requests are just as easy to read for your supervisor and colleagues.
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