You are correct that your datetime value does not have the time component and will not be equal to any other datetime value unless it too has its time component set to midnight.
The trick is to change the if to be a boundary check instead of direct equality:
>declare @time1 datetime
>declare @time2 datetime
>declare @string1 varchar(20)
>declare @string2 varchar(20)
>
>set @time1 = getdate()
>set @time2 = '01/30/00'
>
>
>select @time1
>select @time2
-- if @time2 >= @time1
if @time1 >= @time2 and @time1 < @time2+1 > begin
> set @string1 = "Your the Man"
> select @string1
> end
>else
> set @string2 = "Your the Woman"
> select @string2
This is really only reliable when the datetime does not have a time component.
-Mike