SELECT CASE WHEN CAST(date1 AS DATE) <= CAST(date2 AS DATE) ...
Should do what you need.
Test Case
WITH dates(date1, date2, date3, date4)
AS (SELECT CAST('20101231 15:13:48.593' AS DATETIME),
CAST('20101231 00:00:00.000' AS DATETIME),
CAST('20101231 15:13:48.593' AS DATETIME),
CAST('20101231 00:00:00.000' AS DATETIME))
SELECT CASE
WHEN CAST(date1 AS DATE) <= CAST(date2 AS DATE) THEN 'Y'
ELSE 'N'
END AS COMPARISON_WITH_CAST,
CASE
WHEN date3 <= date4 THEN 'Y'
ELSE 'N'
END AS COMPARISON_WITHOUT_CAST
FROM dates
Returns
COMPARISON_WITH_CAST | COMPARISON_WITHOUT_CAST
Y N
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