(And to be pedantic, #1 returns TRUE / FALSE while #2 returns <int> / NULL, so they aren't exactly equivalent. If you are able to handle <int> / NULL, you don't need the EXISTS clause.)
Leaving the limit in place, without exists #1 returns either an empty set or an <int>, never NULL.
Always returning a Boolean seems like a better API choice though; but standardizing on that final transform doesn’t change the base comparison.
David J.
