Although without testing it I can't quantify it, I think the first would perform better, my rationale is that it should be a fairly simple math operation where only the numbers to the left of the decimal would be evaluated.
To prove the second item won't even work:
DECLARE @test-2 datetime
SET @test-2 = GETDATE()
SELECT CONVERT( datetime, @test-2, 112 )
GO
I think you'd have to convert it to text to do the comparison and text operations are going to be more expensive..
If I may offer an alternative, can you add a calculated column that filters off the time and is set to persisted, then you could do a direct comparison and the cost of the stripping of the date would occur a single time for each record at the moment of insertion.
CEWII