What is the optimal way to compare dates in Microsoft SQL server?

Converting to a DATE or using an open-ended date range in any case will yield the best performance. FYI, convert to date using an index are the best performers. More testing a different techniques in article: What is the most efficient way to trim time from datetime? Posted by Aaron Bertrand

From that article:

DECLARE @dateVar datetime="19700204";

-- Quickest when there is an index on t.[DateColumn], 
-- because CONVERT can still use the index.
SELECT t.[DateColumn]
FROM MyTable t
WHERE = CONVERT(DATE, t.[DateColumn]) = CONVERT(DATE, @dateVar);

-- Quicker when there is no index on t.[DateColumn]
DECLARE @dateEnd datetime = DATEADD(DAY, 1, @dateVar);
SELECT t.[DateColumn] 
FROM MyTable t
WHERE t.[DateColumn] >= @dateVar AND 
      t.[DateColumn] < @dateEnd;

Also from that article: using BETWEEN, DATEDIFF or CONVERT(CHAR(8)... are all slower.